All domestic litigation depends on the jurisdiction of the “Juge aux affaires familiales”. In each French “Département” (French administrative division more or less equivalent to a British county), there are generally one or two Court, grouping several “Juges” specialised in domestic issues.
If both spouses live in France, it is the Judge closest to the residence of the children who will have Jurisdiction. If there are no children it will be the Judge of the residence of the defendant.
In trans European cases, when one spouse lives in a EU country and the other in another, the question is more complex. This matter comes under Council Regulation No 2201/2003 of 27 November 2003. In compliance with this Regulation, spouses can sometimes have the choice between the two legal systems. The usual residence of the children will also be taken into account. In this delicate matter one should seek the advise of a legal practitioner.