The French offer to extend their nuclear umbrella seems to me to have two purposes:
1. Deal with the immediate vulnerability opened by questions over U.S. Article 5 commitments to NATO
2. Try to get ahead of potential nuclear weapons proliferation among other EU states
Certainly France is competitive when it comes to ships and many expendable munitions, but they aren't selling F-35s and the US is, and so far it seems that the juice is worth the substantial squeeze when it comes to that jet. The race is largely for second, because first place (the Lightning) is so far in front of the pack.
They will hopefully purchase Eurofighter or Rafale or whatever else in the future.
[1] (fr) https://www.lemonde.fr/international/article/2022/03/15/la-d...
In fact I think it was the US army that complained about the F-35 being way too expensive.
To say it was underwhelming would be an understatement.
Is it explicitly nuclear?
For conventional war, probably. For nuclear, will Paris risk its homeland for Latvia?
A 'European army' would be under the control of... the EU? Some new organisation to be specifically created for this purpose? Some committee-designed scheme of rotating leadership between the main powers in Europe?
These are not spurious questions. Europe is a large and diverse place, far more diverse than e.g. the USA. Would such an army serve to protect Hungary as well as Spain, Sweden as well as the Czech republic, Poland as well as Germany? Even if some of those countries do not care to fall in line with the agenda set by the Eurocrats in Brussels?
I know that many like to complain of Europe's bureaucracy, but we're talking about half a billion educated people, with enough resources and with an existential crisis, which we're surely facing, the EU+UK, joined by allies, can be a force to be reckoned with.
The problems EU is facing come from within. We have far right movements as well, aided by propaganda, the pandemic and the immigration waves. The far right are more contained than in the US apparently (due to US having just 2 parties), but it can lead to government paralysis. Seeing the US administration ally itself with Russia to dismember the EU wasn't in my cards.
So, it's going to be an interesting year.