Pack a bathing suit or not?

Up to you. Max day temp is around the lower seventies with sea temp a bit less

I was in the South of France the first week of October a few years ago. We were in a beach town on the Med a bit north of the Spanish border. I didn't bring my suit and I regretted it. There were plenty of people in the water.

If you stay at La Fiance' du Pirate in Villefranche the pool will be the perfect temperature for swimming!!

Of course! Better than having to buy one if it is indeed warm enough.
And weights nothing. You can take half also...ha ha

Again my favorite adage:

Tis better to have it and not need it than need it and not have it.

We were in Nice late Sept, and tho the beaches weren't full of people (I'm assuming because it was Sept and not July), there were some out in the water. I didn't go down and test the water, but I can tell you I started the day with a light cardigan and a camisole, and by noon, I said darn the spaghetti straps on the cami, it was way too warm for the light sweater. A bathing suit takes up so little space, I'd take it...

We pack light and I didn't want to take any extra weight, but the suit will be in the bag!

If "we" involves a male partner he should bring a speedo-style suit. Some pools require them.

It's a rule of the universe: if you don't take it, there will be a heat wave; and you'll want to swim. Likewise with umbrellas and rain, except it's much easier and cheaper to buy an umbrella than a bathingsuit, especially in late September.

Yes, bring it. I have enjoyed swimming through October at various regular swimming spots around the Mediterranean and considered the water quite warm where it's either fairly shallow or protected.