The ability of a French resident to get a French mortgage is related to their income. A new tax change appears to be coming in France from January 1st 2018 that will change how much money a buyer can borrow.
According to this article in French in Le Figaro from January 1st 2018 taxes will be levied directly on wages which will effectively decrease the monthly income of many French taxpayers.
The exact rules of this tax application is not in place yet but if the current banking system debt to service ratio that is based on monthly income remains the same the new rules will reduce the borrowing capacity of buyers, according to the founder of Immoprêt Ulrich Maure.
Contact your French tax or banking advisor for more details.