This may be doable but you guys will have to move fast.

When you leave the port, head to the Ajaccio Office of Tourism (almost across from the port) and tell them that you want to go to the nearest beach that offers paddle boarding (SUP). (They speak English at the Tourist Office).

There may be some places in Porticcio or on the beaches of Isles Sanguinaires, both located near Ajaccio.

You can get there by bus or taxi but since your time is limited I would recommend a taxi.

SUP places seem to keep popping everywhere but some of those spots may not a have a web site. That’s why you should ask at the Office.

There is one place in Capo di Feno (north of Ajaccio) however you’re probably going to need a rental car or a ride for that.

Capo di Feno Water Sports
http://www.caposurfclub.com
http://www.corsica-windsurf.com/en/xtrem-sports/clubs-corse/capo-surf-club (map and photos)

Enjoy your trip and thanks for stopping by!