If she is headed in an IR direction then 1) the language skill is critical and 2) learning how to adapt / cope with being in somebody else’s culture is essential.
It’s hard to generalize in a helpful way, but finding a situation depressing- even if it is challenging!- is not inevitable. Being an outsider / newcomer does require putting yourself out there in a way that is not familiar to a lot of people. However, if your daughter is willing to try things, to not take it personally when people have different cultural cues and expectations than she is used to, to explore and find adventures even if she has some on her own, it won’t be depressing!
I’m not sure what it is exactly about “Paris culture” that has you all so anxious- for somebody with good French it shouldn’t be any harder than London (perhaps the similar language of London fools people into thinking that they get British culture more than they do?!).