No, you don't get the "Frog" vote if fundamental national sovereignty is ceded. France will have a veto, or the French people will vote "Non", no matter what clever phrase is used to package the offering.
If they are going to boast that the EU has a larger economy, population, and military than the United States, then they should have only one seat in the UN, make unified military decisions, and protect themselves.
And NAFTA has a larger economy, and almost the population, of the EU.