There were fears at the height of the cold war that the US wouldn't launch their nuclear weapons if soviet tanks literally entered Paris because of the resulting mutually assured destruction. This lead to the formation of ideas like the tripwire force [1]. If you're interested in such topics, I can recommend "The Strategy of Conflict" by Thomas C. Schelling.

If there were credibility problems then, when America was on a much more martial and pro-free-europe footing, the situation is hardly any better now. Although there is a lot less fear of Russian tanks entering Paris, certainly!

[1] https://en.wikipedia.org/wiki/Tripwire_force

For France, this is a good starting point: https://www.csis.org/analysis/understanding-implications-fra...

Quoth: The Strategic Review focuses on preserving France’s strategic autonomy, which is centered on maintaining and updating a credible maritime and air-based nuclear deterrent

Will France say publicly that they don't trust the US? Not in so many words, no. But given that Trump refused to reaffirm article 5, read the following sentence: At the Warsaw and Brussels NATO summits, France decisively and unambiguously reaffirmed its commitment to NATO’s Article 5 and mutual assistance.

Unless you subscribe to the reality TV school of diplomacy, this is quite clear.