Overall, it's important to remember that France was not a blank slate in 1945, with everybody stunned into a blank slate.
Life went on, people kept playing or came back. Prisoners played in the camps.
After the war, life continued or resumed, the old habits came back, and none of those included baseball or american football.
I'd also dispute how much of the Anglo-Saxon influence in France is actually american. Sure, you have a sliver of America in the culture with movies and some music but, and especially music wise, a lot of what you'd see as Anglo-Saxon influence is actually English.
There's a deep fascination (mutual I shall say) with England, the eternal enemy. A lot of the music for example would come from there, fashion too. America is a young nation, with not much of a history, so less time to influence.
I once heard a saying: Europeans think 300km is a long distance, Americans think 300 years is a long time