"Think about this, though: what was the last major international policy that was constructed around, or assisted by, France?"
The Vietnam War?

Well, what was the last major international policy constructed by China? I would call China more "isolationist" or "neutral" in character than France. Traditionally, that is what they have just about always been too. Yet they definitely have the wherewithal to do otherwise if they so choose. Same with France.
France is the main Western influence in most of Africa (i.e. its former colonies), and the currency of many African countries is in fact the franc (the CFA franc, but I believe it's quite closely pegged to the franc). I believe most trade between the West and Africa passes through France, and the French Community (which includes its former African colonies) is their equivalent of the British Commonwealth. France definitely projects a sphere of influence. Does China? Not as much, although that is changing as we speak.
"I don't think a kind of quasi-neutrality shared by France and the smaller French-speaking states around it should be forging international policy."
While a forum to discuss matters, where states can try to persuade other states to their point of view, is harmless and probably good in most cases, actually voting on things like, should Israel be allowed to secure its defenses against aggression using hard-won territory captured from aggressors, is ludicrous. The Israelis have to deal with the consequences of these decisions far more than the Saudis or Pakistanis, so the latter shouldn't have a say in it. That's just one example.
So personally, I don't like the idea of other nations dictating policy to a nation or nations. It usually mucks things up worse than what they may have been otherwise. The reason for that is that people who are local and more involved in local situations often see things that distant powers cannot (or choose not to see, maybe). It is like meddlesome inlaws that don't know the day-to-day problems of a particular marriage intimately, yet insist on butting in--they often cause worse problems with the marriage if they are taken too seriously. A crude analogy, but often the case. So France shouldn't do it, and frankly NO nation, not even the US, should do it.
Not saying that all nations should be completely isolationist--I'm glad we stopped Hitler--but we should at least have the attitude NOT to be inclined to butt in unless it is our business, or the world is seriously threatened. If the UN is to continue to exist, this understanding should be infused into it somehow (I'm not sure how, but we can think of ways)--history is rife with violence and tragedy that sprang from people, and nations, not minding their own business. Perhaps keeping it as a "safe forum", and not letting it vote on just ANYTHING, is a start....