Following the success of Gallic indie exports like François and the Atlas Mountains, could it be that the age-old English prejudice against French music (which possibly stems from the rattle and tum-ti-tum-tum of Napoleon's marauding drummer boys) is finally being undone? Like the Atlas Mountains, Domino Records' first venture into French indie pop, La Femme have made their move across La Mer Anglais with an explicitly French and unashamedly kitsch ouevre, with nods to their nationality everywhere from their name to the Gustave Courbet-inspired cover sleeve of their 2010 debut EP, Le Podium #1. But for those tempted to pigeonhole La Femme as a band defined purely by their origins, forget it. French they may be, but beyond the nervy Gallic veneer, La Femme's character is far from being defined by nationality alone.

It's a bitterly cold afternoon in February when they arrive in London for the first time, wind whipping frostily around Highbury Corner as they to-and-fro, soundchecking, signing records and posing for photographs Upstairs at The Garage. This is their first performance on British soil, their manager explains in broken English, but there's something remarkable about it all the same: without a record label, the band are here purely on the basis of a self-pumped but modest online presence. "We hope tonight will make them really big," he tells me hopefully, explaining the growing interest in La Femme among the mainstream music press.

For all their aspiration, though, La Femme remain unsigned not out of circumstance, but choice - retaining creative control seems to be the objective at play here. "For the moment we just want to keep making good tunes," Marlon Magnee tells me as we relocate to a dressing room after the photo shoot. "We want to stay in control, so we don't want to sign to a label yet." Given that La Femme have followed the now well-trodden path of self-made success by raising their profile almost entirely online, it's nice to learn that they're keen to keep their original principles intact. That's why they include lo-fi in their description on their Bandcamp page, Marlon explains. "It's not by choice," he says. "We record in small studios, so we're lo-fi. We're recording our first album now and sometimes, if we could record in a big studio – well, we'd take the big studio."

Still, their low-key outlook doesn't hold them back. Despite their decision to shun a record deal, La Femme's humble beginnings, the foundations of which were laid by school friends Marlon and Sacha Got in the coastal city of Biarritz, are becoming a distant memory. After relocating to the French capital, native Parisian Sam Lefèvre was added to the permanent line-up, adding bass and synth to the original duo's thrum of guitar, synth and rapid-fire, chattery vocals. The others - Noé Delmas on drums, Clémence Quellenec and Clara Luciani on backing vocals - complete La Femme's rotating cast. An EP appeared on the internet at the tail-end of 2010, and by the start of the following year, it was time to take the band – and their blend of 80s punk and 60s yé-yé pop, culminating in what they tag "80s French lo-fi surf tropical wave Paris" – on the road.

"We toured the United States," Marlon recalls, seemingly unfazed by my surprise that La Femme went transatlantic so early on in their career. "We met a surfer from California in France and they said we should go out there," he shrugs, smiling as he explains that the band have amassed followers from across the globe, many via the internet. "We know people on the web in all the cities that we wanted to play. San Francisco, Los Angeles… And one woman we met online was a promoter in California. She said she really liked us and could get us to play in a lot of places over there."

But if they're at all smug that about coordinating their own success from behind a computer screen, they don't let on. "It's a new age," Marlon stresses. "It's the future. In the 60s, if you wanted to go on tour or make a record, you would need a manager and all those things. But now, the internet is a very good tool for bands because you can do stuff yourselves. The internet means you can meet people, make connections, find gigs…" He trails off now, his own band his case in point.

It's quite some feat for any band to accomplish so much so quickly, but it feels all the more impressive given that the majority of La Femme's songs are written in French. Marlon's interpretation of their success overseas is simple: listeners from the US and the UK like their songs, he says, because the French intonation is "exotic". The language barrier adds a sense of mystery, too – something the band has deliberately courted. Their choice of name, La Femme (which translates literally into English as 'the woman'), is mysterious in itself. "It's an enigma," Sacha says frankly of the guise, careful not to elaborate any further. With scant information available about the band available online, that sense of curiosity, Marlon tells me, is never far away – especially when they regularly alternate female vocalists. "La Femme is not a singer," he reiterates now. "It changes. Maybe that will change one day, but for now that's how it is. In the United States, we found a singer and she didn't speak any French, so she learned with phonetics. She was singing in French but didn't understand any of it!"

La Femme become animated when speaking about any other obstacles that happen to get in their way. With a tight budget, turning up to play in cities without anywhere to rest their heads for the night is a common problem – but as Marlon explains their predicament, a grin remains plastered across his face. "We don't have anywhere to stay tonight," he says, seemingly bereft of worry. "It's fine though. I'll just write on our Facebook page to see if there are any fans that will have us." Does that work out well for them? He and Sacha nod. "Yes – we stay, and in return we make them crepes."

La Femme play at London's Jazz Cafe tonight, and Brighton's Great Escape Festival on 10th May.
The Le Podium #1 EP is available to listen and buy at La Femme's Bandcamp page.