Cost of Living in Poitiers

Your numbers for Poitiers France are fantasy. You need to roughly double them, and that is before the recent inflation trend.

Apartment (1 bedroom) in City Centre 390.00 €

You won't find that price. You might see prices like that advertised, but those are just to get people to come into the agencies. When a person actually goes to find something those will all be taken. A roommate situation might be found for around 500.

Now that summers have gotten hot, attic apartments in the summer might be cheap. There are no air conditioners here!
I did see a closet over a parking lot - with no exterior windows, for that price last year. Looked like a motel sort of, but much smaller.

There are a lot of scams here. People work the cafes. Most contracts are asking 3x rent for deposit. They also have long terms. It takes a long time to evict someone. And good luck getting that back.

There are no dentists available in Poitiers. You will not factor the cost of going outside the city (or flying home?) to get some basic services.

For students it probably looks like a completely different city. The services people at the university will help them get into a dentist etc. They help in finding housing. Most students get subsidies .. 390+250 = 640 that is getting into a descent room in a sharing situation.

The coast of food is higher than you list. It is unlikely to find cheese for 8 a kilogram. 20 Euros a kg is typical. Beef is more like 20 Euros a kg.