Can I rent a car in Normany on a Sunday?

Did you search Auto Europe? They will pull from multiple rental agencies so you'll have a better chance of finding an office that's open. There is perhaps a chance you could rent from the Hertz in Bayeux on a Sunday, it's basically just a gas station that rents cars, but I don't know that with certainty and I don't think it shows on the Hertz website as being open on Sunday. I haven't found any Sunday openings in my searches but that's not to say there not a way...

ETA: If you're arriving by train on Sunday, can you just wait till the next morning to get your car, or do you have somewhere you need to drive that day? If you're staying in Bayeux, it's pleasantly walkable, and the train station is not that far from the center.

You can rent using the service that SNCF has with Avis that makes cars available at certain train stations as long as the station is open. Basically, a station employee handles giving you the keys and the paperwork. I've done it and it worked well. I suggested this to someone on this forum and I believe he reported back that it worked for him.
Also, some rental companies for an extra 60€ or so will arrange for an employee to hand off the car on a Sunday. Sadly, the only person I know who did this was very disappointed because the employee forgot and never showed up.

I suspect that renting a car in Bayeux on a Sunday may not be possible. As a previous reply mentioned, it's just a small operation and they may not be open every day. Renting in Caen is more likely as it's a larger centre, but you'd have to confirm that.

One other note to mention.... for driving in France each driver listed on the rental form will require an International Driver's Permit which is used in conjunction with your home D.L. In lieu of that, France will also accept a notarized translation of the terms of your home D.L. in French.

A few years ago we rented a car in Caen on a Sunday. I believe it was with Europcar. It was arranged before we left the States. We took the train from Paris, walked across the street to a hotel, and the clerk had the key and information for us. The adventure began when he told us where the parking lot for the company was. We got there and did not find a car with the correct license plate. We back tracked and began looking at cars parked on the street and finally found the right car.

Thank you all for your responses. I did a little research on AutoEurope and it looks like I can rent through Hertz at the City Office in Bayeux. which is open on Sundays from 8-12 and 2-5.

The smaller towns rental agents tend to have less open hours than bigger cities. If you can get a car on Sunday, it's likely to be near the train station. One thing I've found is to adjust the time of day you are searching. Look between 10 am and 5 pm, but not during the typical long lunch period (11:30 to 2:00). I've found that if I asked at noon, a search would say there is nothing available. If I searched at 10 or 2:30, however, some places would pop up. Good luck.