To remove all French pices from play was an alternative suggestion, but a changed turn order would likely need some setup tweek here and there. Elseway, if all French are replaced by british, you can’t let UK go before Italy. Italy would be a no Factor in the game, such as the just removed France. On the other hand, Germany would face a harder stand against the stonger UK and less money to spend on turn 2, so a longer fight against the USSR. This could offset the Major advances Italy would probably make.
But my main suggestion is:
-France is after the fall of Paris still able to collect income and may use the UK-London Industrial complex as if it was a minor, French, Industrial complex.
NO for taking Paris for Germany (+5 IPC/Turn) and even an NO for Germany for taking London (much harder if French could build in London +5 IPC/Turn).
With the French income (~9-13 turn 1, ~6-7 every turn thereafter), the allied player would a) be able to build a defense for the UK, b) British money wolud be freed up to produce something more useful, c) French units such as transports, Bomber, Crusier, destroyer, submarines etc. could get used, d) a little more action in the atlantic even without major intervention of the US possible.
Last but not Least: The French pieces in the game are useless. France is almoust never able to build something, in the rare cases it can, it will build at best Infanterie, Artillery, Armor, Fighter. And its not a Major game change either.
Why: Historically, almoust every european country, occipied by Germany, had an exile gouvernment in London and lots of volunteers fougth against Germany from their new homebase London/UK (people from Poland, Norway, France, Danmark, the Netherlands). I think it would be nice to reflect this by those small forces the French player could build.