Using an esim card?

Yes, they work. I have successfully used Airalo eSIM twice in France, also Portugal and Germany. Download the app and follow the instructions, it's simple. Your phone must be unlocked to use an eSIM.

Check that your phone allows you add an eSIM. We have iPhones in my household. My husband's phone doesn't allow him to add esim because it is "locked" (he got through our phone provider). Mine is unlocked, so I have not had any issues.

You keep your original phone line, but you get a new data plan for cell phone service. You don't get a new "number".
Once you are traveling, you switch your settings for cell service to use data from the eSIM plan. I remember the first time it took me a bit to understand which setting to change or keep. And I use wifi when available.

I have used the eSim from Nomad for a few years now. They have country specific and also regional plans. I've used successfully in Scandinavia, Europe, Morocco and South America.

We use Airolo.; I recommend buying a $5 local esim to practice loading it, turning it on and off, etc. Their tutorial video is good.

The idea of a practice run with a local eSIM is a good one if you have a tightly scheduled itinerary and every minute is going to count. However, I've learned from experience that the installation instructions for at least Airalo's eSIMs can vary somewhat from country to country. They are never difficult, and they are clearly explained, but you do have to read and follow the specific instructions provided for each country. It doesn't necessarily work to follow the same steps in Country 2 that a US eSIM might require (voice of experience here).

I am not the world’s most tech savvy person but this YouTube video (https://youtu.be/Pi1Cb1tEeSI?si=vH5IVj9bt2fqXJCd ) made installing an Airolo eSIM so easy for me. I would suggest watching it before purchasing one just to get the idea of what to do. Keep in mind it is a couple of years old, but the gist should be the same if not identical.

Good advice.
A small nit to pick:
A SIM card is a physical card, it's inserted into a slot or a little carrier in the phone
An ESIM is not a card, it's a bit of data downloaded from the seller, and stored in a special place in the phone. The data is normally loaded into the phone by taking a photo of a QR code provided by the seller.

When you look at a vendor's website, sometimes they will sell both SIM and ESIM. Be sure you chose the one you need.

I’ve used eSIMs for short Europe trips and they’re definitely worth it if your phone is unlocked and supports eSIM. For a 10 day France trip I’d probably keep it simple and buy before leaving, install it at home, then switch mobile data to the travel eSIM after landing. One thing I’d check is whether you only need data or whether calls/SMS matter too, since a lot of travel eSIMs are data only. If you want something with a number and some calls/texts as well, eSIM.net has France options that are worth comparing with Airalo/Nomad before you buy.

Absolutely, eSIM cards function well provided that you have an eSIM enabled device that is unlocked. For a 10-day journey, Telefy is highly recommended, as 5-10 GB will be sufficient for your needs and unlimited data will suit heavy users.

While you use the eSIM, can you still get texts and phone calls from people who call your regular line from the US?

I am in Australia, not the US, but yes, if I leave my main line turned on, but turn off data roaming, I can still receive calls and texts as usual.

The problem comes if you answer the calls, that can then get very expensive, but getting texts with bank codes and so on is completely free.

Thank you, Deb! That is very helpful!

I'm sure what DebH said is true for her, but for many cell plans there is no International Roaming. And if there is, the prices per text or minute may be well above zero. You really need to read all the fine print in your plan regarding international Roaming.

Travelerguy, I did point out that I was in Australia so things might be different.

I think all phone plans can receive texts without charge, certainly all ours can. Sending one though is a different thing.

Once again I'm compelled to mention esimdb.com, which is a brand agnostic site with a handy database of available cell plans in Europe and elsewhere. It's always worth checking out.