When do I need to buy train tickets from Paris to Avignon for mid May?

You can and should buy them now. Some tickets around 19 May (the 18th is a holiday, many people take a 4-day weekend, myself included) could already be scarce. SNCF Connect is where it's at. If you can't work your way around that website: check out "the man in seat61" website for instructions; trainline is a good backup agency for a very small fee.

By the way, there are two stations in Avignon: Avignon TGV and Avignon Centre. They are linked by local train, so you can just put Avignon Centre as your destination. Most connections will involve going to Avignon TGV and changing to that local train, but there is a daily train that goes directly to Avignon Centre. A bit slower, but worth it IMO.

Just here to underline / support the advice that Balso has given. Spot on.