@Marcin Hey Marcin, what an irony! I got accepted into BU as well. I wouldn't worry too much about if it's suspicious. They don't interview candidates in general. Some programs do, others don't so I wouldn't worry. Congrats!
Also, I do know where you're coming from. I come from a family of professors but they are specialized in politics, biology, law, finance, and international relations. They have all ended up at fabulous places with tenure-track positions and some even higher (in government positions). Looking at them, I wouldn't worry but I do since this is a French PhD, not a Politics PhD. I'm paranoid that I might lose financial stability by following my passion. At the same time, like you, I don't like the job I'm in. I think it's a matter of tossing up which matters more to us: taking a risk or sticking to what we have. I'm confident we'll find our way either way!
When I say this, I don't mean to put down fellow French PhD candidates. We come from very different backgrounds. However, a little compassion will go a long way. After all, what is the point of becoming a professor if you can't compassionately connect to students.