Evidently, the ban actually goes back a long ways, well before the advent of the modern long-and-baggy style, and it has more to do with cleanliness than flapping fabric.
As I understand it (based on things said to me by more than one French person), the rise of city industry, especially the automobile, led to concerns that people walking off the street into la piscine were dusted with soot and grime, and a full change of clothes and a pre-swim shower would be required before diving in. And to ensure that someone wasn’t just keeping on their “street shorts,” the rule about small and snug swimwear was conceived, because there was no way anyone would be wearing that little thing while out and about in town. In other words, there had to be an obviously pool-specific garment that would only ever be worn in the pool, with the underlying intention of helping to keep the water clean.
This is why, if you ask today, the catchall justification about this practice is that it’s “hygienic.” If you don’t know the context, that seems like strange reasoning, but with the historical background and the aim to prevent outside filth from swirling around in the pool, it does make some sense. And certainly, the same reasoning would continue to hold, if the intent is to create a procedural barrier to street dust impacting water cleanliness; you don’t want your tourists strolling down the car-clogged boulevard in Nice and then jumping straight into the hotel pool wearing the same trunks.
I’ve done some googling off and on over the years trying to confirm the legitimate historical veracity of this tale. The explanation above certainly seems to prevail in the modern dialogue, but I haven’t found anything reliable that carries the same justification all the way back into the 1910s and 20s when the laws were originally created, as my French associates claim. I welcome any more concrete findings either way.