That the hometown of Leonard Cohen, Godspeed You! Black Emperor and Arcade Fire is fertile territory for musicians should come as no surprise. But the recent arrival of Grimes, Suuns, Purity Ring and countless other Pitchfork-friendly buzz-bands has seen the hype increase in volume. Is Montreal really the new Brooklyn? How did a French-speaking city become a North American musical colossus? Perhaps it's due to low rents, grants for musicians and the proliferation of universities. Or perhaps this new wave of great bands is simply the latest installment of the bumper reparations package Montreal owes the world after poisoning our souls with Celine Dion.

POP Montreal, now in its second decade, is a multi-venue, city-wide celebration of popular culture from around the globe, although a high proportion of the performers live and record here in the province of Quebec. The size and scale of POP means stage-hopping often involves bus journeys and Metro rides. The clashes are horrendous - it’s probably the least FOMO-friendly festival I’ve been to. But in Mile End, probably the coolest place I've been to - if coolness is measured according to quantity of inappropriate footwear at gigs (wellies? really?) - it's easy to walk between venues. Here, the usual hipster elements are present and correct: third-wave coffee, microbrews in no-name dives, 24-hour bagel bakeries, indie-rock launderettes, vintage clothing superstores... and suspicious glances towards posh furniture stores; whispered conversations about encroaching gentrification. Vice launched here in the mid-Nineties and clearly left its mark, but parts of Mile End are increasingly looking like Wallpaper*.

One element of Mile End hipsterdom will look unfamiliar to those from Williamsburg, Echo Park or Dalston - the French language. It’s on the street art, the gig posters taped on the trees, and on every shop sign (Quebec law dictates that shops must have French in a larger font than English). I’d read that relations between the English and French 'communities' in the province are frosty; but although Montreal is 90 per cent Francophone, in the venues I hear a 50/50 split and often the languages intermingle in a playful Franglais.

When it comes to the bands there’s something of a paradox. The city’s reputation as a creative hub has lured musicians and artists from English-speaking Canada and the US, so while bus drivers, bank clerks and supermarket staff speak to you in French, the majority of bands sing to you in English. Although they’re heavily outnumbered on the line-up, a few Francophone bands are involved and I’d been told that Avec Pas D'Casque shouldn't be missed, but when I reached their show at the incongruously uncool Ubisoft offices there was a note, in French only, apologising for the cancellation. I headed straight to Les Trois Minots, a dive that wears Coors Light posters without any apparent irony, to watch hotly-tipped local quartet Les Jupes, but moments after walking onstage the singer declares that none of the band speak French. Their literate, dark, synthy songs (one is about Nikita Khrushchev, no less) deserve better than a turnout of 15 people, and their recent album Modern Myths is a hidden gem.

An equally tiny crowd watches Toronto’s Revelstoke, the alias of Andrew Seale, perform a short set of woodsy, fragile folk at Place Pasteur - a leafy piazza downtown. With a banjo, loops and ghostly vocals, he performs songs from his debut Esprit d’Escalier as well as a song not yet five minutes old; a poem written by a man sitting on the street with an old typewriter, tapping out free poems for passers-by. The presence of burgers and beer helps lure a much larger crowd to a showcase of local acts in a park in Little Italy, a neighbourhood characterised by Fifties time-warp cafes - old Italian chaps drink foamy macchiatos while watching Serie A. I’m underwhelmed by Toronto's Warp-signed band Born Ruffians, but captivated by Calia Thompson-Hannant, aka Mozart’s Sister, whose part-Grimes, part-Tune-Yards, part-Kate Bush approach to songwriting seems genuinely fresh, even in a city where female-fronted electro-pop outfits are a dime a dozen.

I can’t get into the sold-out Grimes show so I settle for the next best thing, a performance at the intimate La Tulipe theatre by the prodigiously talented Purity Ring. Corin Roddick and Megan James concoct catchy, complex pop that falls somewhere between Bjork at her danciest and Beach House at their dreamiest, with R&B stylings thrown in for good measure. Roddick plays a self-made instrument, a tree of eight touch-sensitive lanterns he bangs like drums; they change colour according to the notes he plays. They’re more exciting than another local dream-pop band, Young Galaxy, who perform in the comfy confines of the Breakglass Studios, where the recording alumni also includes Sunset Rubdown, Patrick Watson and The Besnard Lakes. Despite studio-perfect acoustics and a partisan crowd, most of whom seem to know the band personally, their songs seem cold and generic to me.

The latest batch of Montreal bands are expert at finding that sweet spot where chart pop meets the avant-garde, but I’d have like to have seen POP give more exposure to the city’s experimental label stalwarts. Constellation (Godspeed, Thee Silver Mt Zion, Do Make Say Think) and Alien 8 (Set Fire To Flames, The Unicorns) seem under-represented, but at least Tim Hecker is here to perform with rumbling, sprawling aplomb, and nearly take the roof of the beautiful Church of St John the Evangelist. His show follows a confident set from young Montreal duo Solar Year, a kind of warped, slowed down, Auto-Tuned version of Perfume Genius. The local bands sandwich one of the most gorgeous sets of the festival, a pared-down cello-and-piano show from Julia Holter. Her voice is buried quite deep in the mix on her records, but in this setting is becomes clear what a powerful instrument she possesses.

One of the most distinctive voices of the festival belonged to 75-year-old pimp-suited blues legend Andre Williams. The nonchalantly spoken lyrics to ‘Bacon Fat’ still sound singular; it must have caused quite a stir upon its release back in 1957. ‘Jail Bait’ gets cheers from the crowd despite its Jerry Lee Lewis-ish subject matter, and after a raucous closer in which Williams repeatedly informs us that he's a "bad motherfucker" - and nobody dares disagree - the Detroiter calls it a night and leaves us with his backing band, The Sadies, who are brilliant. The Toronto group play classic country and surf rock with the pace and fury of a garage band.

Elsewhere there’s a fantastic set from Zammuto, the new project of Nick Zammuto, formerly of The Books. A slot supporting Gotye at the vast Metropolis Theatre seems an odd fit for such a relentlessly creative musician, but his band’s proggy, percussive songs win over the festival’s largest contingent of teenage girls, not least because they’re accompanied by hilarious videos on subjects as varied and important as chronic back pain and zebra butts. Los Angeles duo Lucky Dragons have a more po-faced approach to AV. Their show at Centre Phi, an interior design geek’s dream of a contemporary art centre close to the magnificent Notre-Dame Basilica in the old town, sees members of the audience invited to use CDs to reflect rays of light and create new sounds. Such gallery-grade pretentiousness is offset by the sight of kids waving CDs in the air, making swooshy sounds and feeling like rock stars.

I did, however, catch one show of inexorable wank. The three members of Title TK carry their instruments onstage but never get round to playing them, instead getting distracted by conversation about mobile phone tariffs and Twitter. It’s funny for about three minutes. After half an hour, it's a cheap prank that's long outstayed its welcome. But it’s a rare flop. At the L’Olympia concert hall, Grizzly Bear’s epic performance suggests that Brooklyn isn't about to concede its status as indie-rock’s indie-est city to its Quebecois challengers without a fight. It seems remarkable that the depth and subtlety of new album Shields can be rendered so perfectly in a vast, echoey 2,800-capacity venue. Their support, Unknown Mortal Orchestra, impress with fuzzy, distorted psych-jams. Other star performers from the States include Deerhoof, whose muscular, jerky, heavily punctuated rhythms are in striking contrast to the sing-song repetitions of frontwoman Satomi Matsuzaki. A set featuring songs from throughout their 18-year career goes down well with a overwhelmingly hirsute Mile End crowd.

Speaking of facial hair, Warren Ellis of the Dirty Three is on scintillating form down the road at the Ukrainian Church. He screams and yelps, tells hilarious stories about Paul Hewson (Bono), Paul Gadd (Gary Glitter) and Paul McCartney living in a colony of evil Pauls, and plays the violin like a man possessed. Alongside his shamanism, bassist Mick Turner's statuesque, straight-faced professionalism seems drolly comical - and then there's Jim White, painting the drums. When Warren goes widescreen with soaring riffs and kung-fu kicks, Jim is balletic, yogic, metronomic; all space and light. And when Warren plucks strings, hammers keys and induces claustrophobia, it's like watching a close-up magician on the sticks - a nimble-fingered juggling act, a masterclass of texture and control.

The eclectic line-up [I missed plenty of hip-hop, dancehall, techno and everything in between], as well as fashion shows, stand-up comedy, films, craft fairs, art shows (including - gasp! - the chance to sit in the car from the cover art of The Suburbs) and music industry talks - reflect not only the uniqueness of North America’s only truly bilingual city, but also Montreal’s energising diversity.