"The EU is popular in France. "

LIE.

http://www.pewglobal.org/2016/06/07/euroskepticism-beyond-brexit/pm_2016-06-07_brexit-01/

The French support the EU LESS THAN UK CITIZENS!

The French are 60% against the EU, while in the UK it's only about 50% - and that caused Brexit.

EU support is falling across Europe and has been for a decade.

(The chart above shows current sentiment, but the trend is all down since 2004.)