What is the ruling on remaining in a non-Muslim country—France—after completing studies, for a non-mandatory professional training, or for permanent employment? And does this fall under the hadith: "I am free of any Muslim who resides among the polytheists"?

Emigration (Hijra) is obligatory if a Muslim is unable to practice their religion in a particular country, but it is not obligatory if they are capable of practicing their religion. Rather, it is desirable, and staying might even be preferable if there is a compelling benefit.