I think this, French orientated, opinion piece clearly sums up the French strategy and views. It does reflect the French view of themselves as a global, and especially Indo-Pacific, power where it seems to see itself as an equal participant to the USA and China.
https://www.thelocal.fr/20210918/opinion-frances-australian-submarine-row-shows-that-macron-was-right-about-nato/
OPINION: France’s Australian submarine row shows that Macron was right about NATO
Some of the views expressed above are driven by considering Reunion and New Caledonia as integral parts of France whilst most (including the USA) would consider them colonies.
If you have read into the strategy of the USA both during and post WWII you will know they despised colonialism, especially in the Far East and Pacific and the dismantling of the British, Dutch and French Empires, as they saw them, and particularly decolonisation were an essential part of their plans.
I can well accept that view still holds in Washington and the "slap-down" by the USA has been deliberate.
The UK lesson learnt after Suez, as expressed by MacMillan, was that it was better to be an ally of the USA rather than opponent, that learnt by DeGaulle was that France had to be able to stand alone - one reason, as previously noted, he withdrew militarily from NATO in 1966.
The tome of the above article, when seen in the light of French comments in the last few days, is that Macron intends to emulate DeGaulle. If the French see their only way ahead is to attempt to build an alternate EU power base independent of the USA then the comments being uncertain future of NATO are not unfounded.