Pretty sure you could engineer France leaving the EU by just tweaking fishing quotas, farming subsidy, naming on sparkling wine or removing (as you mention) strasbourg. They will start a riot and then when you don't give in, they'll be gone.
I'm not saying it's what happened to the UK, but we asked for what we needed, got turned down and then left.
I think it was a ban on European migrants from sending benefits and particularly child benefit (some money you get from the state if you have kids) back to thier home country or something like that.
I remember Poland stopped us from getting it (supposedly).
The french didn't want us to exempt from financial regulation that was primarily targeted at the euro even though we use the pound.
Various nonsense, that people at the time felt strongly about (keeping the pound, not giving benefits and a council house to people as soon as they arrived, or some such exaggeration)
I don't get why the EU can't be just a big common market with free competition, open borders. Why do we even need lots of institutions, bureaucracy, directives on top of directives and quotas for farming and fishing?
I'm not saying it's what happened to the UK, but we asked for what we needed, got turned down and then left.