Not to sound like a scold, but if you’re an expat and you’re not making significant efforts to speak the language and learn the culture, you might be doing it wrong. I lived for a long time in Italy and the experience was *definitely* enhanced by *trying* to speak decent Italian (by the end of my time there I almost could, even).
For me, this meant watching Italian TV, taking Italian language classes, going out of my way to make Italian friends, so on and so on and so on.
Also, embrace the lifestyle, even if you feel like a fraud. Poverty taught me how to shop like a local and eat like a local because the good stuff is generally what the locals eat (and it’s cheap). Tony Bourdain taught us all that. Not that there’s anything wrong with poulet roti, the French have made that (as so many things) into an art form.
For me, one of the joys of living in Italy was learning how local people navigated life, what they celebrated and how and when they celebrated it. This included mundane things like how they take out the trash, which for an American was pretty enlightening. It also included cadging an invitation to help with the grape harvest (vendemmia) at a vineyard owned by some friends of friends, and one of the best parties I’ve ever been to.
All that being said, you’ll never be French, of course. Part of being an expat is being an outsider. Of course, that’s what expat groups are for. Also, you will always be the slightly exotic (less so in Paris perhaps, but still) foreign friend.
I’ve also found Paris to be lively and charming. And friendly, even. My French is pretty bad, verging on terrible. I’ve never consciously hidden my Americain-ness. But I’ve never understood the many tropes that my countrymen have launched against Paris. It’s their New York. It’s the Big City, for good or ill. People in Lyons are friendlier (and the food is something else), people in Marseilles will talk your ear off (they just might be picking your pocket while they do it, so…) but Latin culture is generally expressive and fun. And if you want to see punk rock weirdness, head for Bastille — it’s there. Or at least it was in the late nineties (grumble get off my lawn grumble).
Finally, Paris was where I got one of my best compliments. Lost, in the rain, looking for a cheap pension, I asked a passerby where the Rue des Whatever was. He asked me if I was Italian. So apparently my Bad French had upgraded into Bad Italian Speaking French. So I had that going for me!