Please advise what 'free parking means.
Is that parking in a hotel garage or find your own on the street.
If the latter how far away?
We stayed here last summer and had a car. The accommodation has a couple of parks in a small carpark just down from the apartment. It is free but they have limited spots so just make sure you contact them to say you have a car before you arrive. The carpark is also within the walls and literally a 2 min walk from the B&B so was no problem at all.
If you are driving your own car or a rental car, you are probably going to have to park outside the city walls, so the question of parking near the Osteria is going to be moot. Driving inside the walls requires a special permit.
I don't remember having to pay for my (disabled) spot (outside the walls), but if you have to do so it will not likely be horrendously expensive.
It may take a bit of patience to get yourself a good spot, but don't despair.
Get an answer from Osteria del Borgo staff and past guests.