I heard that there might be people renting their own cars at a very low price. Kind of like an Airbnb for cars. If there is, what's the name of the company and where shall I search?
Which town do you mean?
In Paris, there are many, but there are quite a few problems - theft is becoming an issue, as are insurance issues. Google "voitures a partager paris" and take everything you read with a large grain of salt.
Ouicar, Drivy, Koolicar...
If you have a valid driver's license and insurance, you might try subscribing to the AutoLib' plan. which allows travel within Paris.
I would assume that insurance could be a problem. For example, if a friend visits me and I let them use my car, my auto insurance provides coverage. But if I start renting my car as a business, it may not provide coverage.
People in France told me about BlaBlaCar.
It's similar to Airbnb; people who are driving from one place to another advertise for riders - who pay a proportionate share of the cost (gas, tolls).
I tried to use it to get from Amboise to Chartres, because the only train I could find took me into Paris and then back out to Chartres. I couldn't find it on my smartphone, so I ended up skipping Chartres (I'll visit later as a day trip from Paris).
Here's the website: