If Malta takes your fancy, I think the Westin Dragonara there ticks all your boxes. There's not beach in the sense of large swathes of sand, but it is seaside with a private sheltered beach area. You're very near St Julians town and can stroll along the coast easily in both directions. Great local food and baby-friendly cultural sites too. There are direct flights from both Paris and Rome, obviously not the shortest from Paris but the resort is only a short drive from the airport.

Alternatively there are an infinite number of places that would suit your needs in Spain or Portugal, the latter particularly for high end family hotels, and Mallorca is always worth a look.