Morning trip to Giverny then train to Avignon

I can advise on the train-related questions. en.oui.sncf lets you check times and buy tickets, so does www.loco2.com at no extra cost. Trains to Vernon leave from Saint Lazare, trains to Avignon leave from Gare de Lyon.

Neither of those stations are particularly convenient to your hotel; it will take three hours to get from Vernon, to your hotel, pick up your luggage, and head to Gare de Lyon.

The train to Avignon then takes 3 hours, so there's no way you'll have any meaningful time in Avignon that day... Therefore, to avoid being stressed out in Giverny and leave yourself some room to miss a train in Vernon, I'd simply take the last or second to last train to Avignon. They typically leave at hh:37, 18:37 should be fine, 19:37 leaves more room for error if you don't mind an 11 pm Avignon check-in. (or need to pick up a car before agency closing time)

Balso. I can’t thank you enough for your very detailed advise. That is exactly what I needed to know ! Much appreciation. I does make for a long day but. Knowing that and being able to plan accordingly helps tremendously.

Always give yourself more time than you should need when it is critical.

We had concert tickets last night for the Philharmonie in Villette and I had screwed up and booked our Louis Vuitton Fondation tickets the same day so we were kind of running all day. We left an hour to get from our place in the 13th to the Port du Pantin metro on the 5 -- should have given us at least 15 minutes to spare. We were half an hour late to the 8:30 concert because the metro was stalled underground for about 40 minutes -- it stopped for 15 minutes then went to the next 5 stations -- stopping at each for 5 or 10 minutes. There were announcements but you know how garbled station speakers are so we didn't know what was going on. Luckily the Philharmonie has a really great system for getting you in when you are late -- we had terrible seats of course but at least they got us into hear the music.

This is unusual -- but count on the unusual if you have a tight schedule. We have had late trains, late planes, trams that broke down on the way to the train station etc etc -- so usually we leave plenty of time.

Make sure that you check the schedule for the trains for your return trip to Paris. The train that leaves at around 1 PM takes about 2 hours to get to Paris. The other ones take about 50 minutes and the trains run roughly every two hours. I think you should drop your lunch plans to make this day work. Last time I was at Giverny (May 2018), we had delicious sandwiches that we bought just outside the entrance. The other times we have been, we had lovely, sit-down meals at Restaurant Baudy, but we were not trying to get back to Paris to go across town to catch a train.

Note that neither train station is directly where you want it to be. Vernon is very far from Giverny (we managed to rent bicycles, but it was sweaty), and the Avignon train station is just outside the edge of the old city. Is there a deadline time to check-in in Avignon? This is an ambitious program for one day, especially with a quality lunch in a Slow-food country. Month of the year?

Every time you get a new "seat" of public transportation, there is ticketing, stop-finding, and scheduling latency delay. Not to mention unexpected events as one reply notes.

Look for your hotel and Metro stop on Google Maps.

Barbara, Tim and JHK,

Thank you for such wonderful advice! After listening to all your recommendations I think it is probably do able however
We do want to enjoy our time. We will either go the day before or forgo it. I am wondering if anyone has been in August and if it will still have all the beauty that the spring time might provide. Perhaps I take this off my list for this time.

We will be renting a care in Avignon. Have not booked that yet. Can we find that close to the train station?

Much appreciation to all who gave their advice

Why don't you leave your bags at one of the train stations -- I'd say Gare de Lyon and then hop on the Metro to Gare St Lazare for your trip to Giverny. Then just pick up your bags before your train leaves for Avignon. Yeah, it's a bit of a hassle that morning, but it saves you a trip back to your hotel. See if BagBnB has anything in the area. Maybe you could still have time for lunch -- not looking at the train schedules, but I'd definitely eliminate the need to go back to the hotel.

The gardens are meant to look lovely no matter when you visit. Here's a link to the website that gives you an idea of what's blooming throughout the year.

If by "Can we find that close to the train station?" you mean are there rental car agencies near the train, the answer is yes. There are rental car agencies at the Avignon TGV station.