Is everything closed the weekend of Ascension Day in both France and Italy
In France, with some exceptions, most department stores and supermarkets will be open, some supermarkets could open only in the morning.
For small businesses (bakeries, butchers, grocery stores, etc.) it is up to the owners to decide. The vast majority of restaurants, cafes and bars are open as usual
Administrative services and banks are closed and public transport may be reduced as for a Sunday but this is a local decision.
So in fact no big changes, even less in tourist areas
Ascension Day (and some other religious holidays) has not been a public holiday in Italy since 1977. For most (all?) countries, lists of public holidays can be found on internet.
As Ascension is always a Thursday, it will be no different from any other working day.
We were in Strasbourg, France on Ascension Day last year and it seemed that many locals had the day off and were sightseeing as well, so the regional trains were standing room only. We did not notice any restaurants being closed.
It is typically one of the busiest travel weekends of the year in France. Train tickets should be booked asap and driving towards big cities on the following Sunday will be a test of patience. The impact on shops is minimal nowadays.
Pre ATM days, Ascension and similar holidays that were celebrated in some European countries, but not the USA, I always seemed to need a bank on those days.