Rideshare options in Bayeux

I can't speak specifically about Bayeux, which might be an exception given how touristy it is, but rideshare drivers like those for Uber or Bolt are scarce outside major cities (there simply aren't enough fares to make it profitable).
You might also find that when you book an Uber or Bolt, an official taxi registered with the platform shows up.

In truly rural areas, these services don't exist; it's not even worth trying. For many people there, the name "Uber" just sounds like someone named Hubert.

With the distances and rural nature of the DDay landing area, including Bayeux, it would be a waste of time and money for a one-way ride for the driver. If you are looking for someone to take you to a particular sight, say Omaha Beach or the US cemetery, you would do best to hire a guide for the morning or afternoon or day, and go from place to place that way. The sights most people want to see are not next to each other or quickly walkable. The five beaches stretch for 50 miles, and the designated DDay landing area is about 500 square miles. If you want a taxi for Bayeux only, you may find that much of what tourists visit there are in a walkable area, and a taxi may not be needed.

What are your plans for Bayeux? Do you need a taxi from the train station to a hotel perhaps?

Taxi's are barely available. The best way to get around is to rent a car. That's just the reality of the rural location.

Hiring tour guides also an option.

Good advice from Judy. You don't say for where you need a ride, but Bayeux itself is very walk-able. If you intend to see D-day sites in the area, you really must have a car—either your own (preferable) or one provided by a tour guide.

Clarification: Will be staying at a villa about 10 km outside the town and am looking for the best way to get between the villa and the town or to dinner at another location. If it's only taxi, that's fine; I'm just trying to determine my options before I travel. Thanks!

You will need to order your taxis well in advance, as soon as you know your schedule, because there aren’t many, and they are also used as medical transport in France with regular pickups for chemo and pt and doctors appointments.

For your needs a rental might be most convenient.

You're in the countryside and Bayeux is a smaller city. More of a town. A town with amenities, but not with big city amenities. You might need to find a local driving service.

Here are the websites for two local taxi companies in Bayeux, where you can find their contact details.
You should get in touch with them in advance to see if they can accommodate your specific needs. As Elizabeth mentioned, they are often booked for scheduled medical transport, and those in Bayeux can also be hired for tours of the D-Day beaches.

https://taxis-du-bessin.com/

https://taxisbayeux.com/

Another option if you do not have a car, is to rent a bicycle.

Globetrotter,
Not to be a downer, but if possible, rent a car for this portion of your trip, especially since you are not in the town of Bayeux. The posters are correct in that you will need to prearrange all your rides, and not necessarily just the day before. Or find and reserve a driver for each day's explorations.

Just curious, how will you be arriving at your lodgings? Is transport from the train station (I assume you will arrive by train) already arranged? There will likely be no bank of taxis waiting at the station for passengers.

The taxis at the train station will be waiting for the people who pre-booked them.

My in-laws lived in a village 10 kilometers from the small town with the train station. We learned from experience that taxis had to be pre-booked.