Remain.
I agree with L.A.'s analysis.
In addition, I own property in France, which is a borderline basket case with Marine Le Pen's extreme right wing National Front enjoying considerable support from the French people. She may perceive Brexit as giving her policies some kind of legitimacy and French homes for French people may result in separate, higher, property taxes for nonFrench second home owners or even snatching the houses from their current owners for the benefit of homeless French citizens.