At first glance, this movie seemed to be about whether or not a rural French village will accept a (French-educated) African doctor and his family. And that's almost true. It's definitely a subplot. But the real question is whether a (French-educated) African doctor, who does not want to go home to his native country and become part of the corrupt and exploitative system at play there, can convince his wife to stick it out in a cold, unwelcoming, backwards French village where he has talked himself into a job.
In a movie like Remember the Titans, which is about whether or not Whites can accept Blacks, emphasis is placed on how normal the Black characters are, how they are just like their White counterparts, in order to show how utterly ridiculous the White characters are to even consider rejecting them. Not so in The French Doctor. Dad just wants to integrate, to the point of forbidding the speaking of anything but French at home*; Mom just wants to go home, which ends up in a life-altering phone bill; but when aunties and uncles and cousins from Belgium show up, partying in their very African, very non-French way, all of Dad's carefully constructed "we're just like you" facade begins to break down.
This is what I love about this movie. It has the confidence to let the relatives be weird. It's a fish out of water story, but with the fish being Black and the non-water, as it were, being White. And the stakes are integrity and marriage, and I don't know of any higher stakes than that.
One more thing that might help you understand this movie a little better upon first viewing than I did: the narrator, the now-grown son, is in real life a stand-up comedian. The African Doctor is based on a book he wrote about his childhood. I think I might have missed a few jokes the first time, because I'm so darn used to integration narratives being deadly serious. Maybe we could use a few more funny ones, to let us see how ridiculous we all are sometimes.
*To be clear, they all speak perfectly good French to start with, but like most Africans, they have at least one African language they can call upon as well. Dad isn't trying to improve their French; he's just forbidding Lingala for the sake of forbidding Lingala.