From Paris to Aix en Provence

Yes there is Google La Consigne Avignon

Rick Steves France 2020 suggests https://consigne-avignon.fr/, near the Avignon Centre train station and the bus station. There is no bag storage at the Avignon TGV station (though there is car rental).

Speaking about car rental... it might be the best option for what you're planning to do.
I'm assuming you mean Pont du Gard, when you mention the "acqueducts"? Getting there from Avignon TGV station (where you'll arrive from Paris) is feasible but quite a faff by public transport: local train to Avignon Centre, followed by a bus to Pont du Gard.
Then back the same way, with the choice of infrequent but direct bus from Avignon Centre to Aix city center, or TGV again from Avignon TGV to Aix TGV, then shuttle to Aix city center.
I don't mean to scare you: you can do this.

But if you're happy with renting a car for the half day, your life would be much easier. Drive Avignon TGV -> Pont du Gard, then Pont du Gard -> Aix. Parking at Pont du Gard is safe enough with luggage (guarded) but you do need to book a car big enough to put everything in the trunk. A "C" / "Compact" category will typically do, and you're looking at 80-100 euros for the short one way rental, which isn't much more than the bus, train and shuttle tickets you'd need.

You could also start in Nîmes. Same driving time, but car and train prices might differ, so the comparison is worth it.