As for Lepanto, Charles IX was dealing with the leadup to an extremely bloody religious civil war at the time, foreign adventure was one thing France absolutely couldn’t deal with right then.

I will add that in the present day, I’m aware of quite a lot of Franco-German ties on business, family, romantic, and other similar levels. The French don’t mind the Germans, and I get the feeling it’s mutual; the dispute over Alsace has been settled (and in all seriousness it was settled from the start; when Louis XIV annexed it he was met with cheering throngs in every city), the Napoleonic dream is over and done, and there’s nothing else to quibble over. The English, however — there’s a thousand years of conflict there, with the 20th century alliance being one of a few exceptions. Brexit has been met with comments like “they should never have joined in the first place”.

“In addition to the spread of neoliberalism, which, as I stated above, is an ideology corrosive of cooperation”

There is nothing more favorable to cooperation than Neoliberalism.

“…but when they were faced with outsiders (for example, during the Crusades), they actively cooperated with each other.”

Wrong. At the time of the Ottoman siege of Vienna, the French were allied with Turks.

What about the troubles to get the Lepanto Battle to occur and the subsequent debacles?