I just realized that my first day in Paris
will be Ascension Day, May 17th.
Does this mean that shops, museums,
restaurants will be closed?

It's not as significant a holiday as May 1 and May 8. You might find that some shops and museums are closed, but you'll be able to find enough to do (the Louvre, for example, is open). People who do get May 17 off might take the long weekend, so it could be a little more crowded than usual in the train stations and airports.

No, it doesn't mean that. Restaurants never close for most holidays, anyway, certainly not that one (probably the most for Christmas Day). And museums only close on a few major holidays, and that isn't one of them.

The only really big holiday in France is May 1st.

Most other holidays, banks and post offices are closed, some shops may be closed, but all tourist activities are in full swing. On Ascension, the department stores and most other stores will be open as usual. So will museums.

What holiday is May 8?

What's May 1st? I'll be there then..

Wait, nevermind, just realized that's Labour day..

May 8th is VE Day.

And many Americans are surprised at how much closes down on Pentecost, sometime in June. I know I was.

No need to be surprised about that anymore. Pentecost is no longer a holiday except in Nimes.