Ecolodge Le Hameau des Pesquiers (Curio Collection by Hilton)
The pool. Nuxe spa with heated indoor pool and hammam, the beach a few metres away, according to Staycation.
I haven't yet found guest reviews that mention the water temperature. Expedia shows 9.0/10 from 38 reviews.
Guide's tip. The covered pool lets you swim whatever the weather on the peninsula.