They’re only unwilling in the context of it being part of NATO.
They have been joining the militaries of neighboring countries to the Bundeswehr for a number of years now, particularly those of the Netherlands and Slovenia. It’s part of the overall plan to unite all EU military forces under one aegis.
As for England, remember Brexit? And France is very, very friendly towards Germany in terms of military unification, even once offering Germany the use of French nukes if need be.
With one very important proviso you're not mentioning:
"Non, non, mein Herr! You misunderstand! Eef you wish, we will deploy ze Bombe Francais - Eh, bien, 'ow do you say? - on your territory!"
Yes, the French told the Germans that the French would happily A-bomb any target on German territory for them. (The idea was: To destroy invading columns of Soviet tanks.)
With friends like that...
Regards,