Is this too crazy of a schedule for basically one day in Provence?

To answer your question...Yes! Doable if there is no traffic, if a parking spot is available right in front of where you are headed, if you get fast service and eat fast for coffee/pastries and lunch. You have 1 hour and 15 minutes seeing the Chateau de Lourmarin AND having coffee and pastries, leaving there at 11:00 to be at Bonnieux & Roussillon by 11:15. If you get to Senanque at 2:30, and leave at 3:15 to get to St. Remy by 4:00. that also makes for a short visit to the Abbey. And if at St.Remy at 4:00, you have 1 hour and 10 minutes to explore it before leaving to get back to your hotel at 6:00. It sounds exhausting, and you won't have time to enjoy the scenery of Provence.
Also, the sites that provide drive times (Google, ViaMichelin, etc.) all underestimate the time. They don't allow for gas or food or bathroom stops. The country/small roads between these towns may have single lanes each way, and if you get behind a farm vehicle, you won't move fast. (I speak from experience.) Also, even on some smaller roads, there may be speed cameras. There is no leeway above the speed limit in France, as there is in the US. You could receive a ticket six months later in the mail, as well as a charge from the car rental company for providing your info to the ticketing agency. Best to relax and not try to cover too much territory in too little time.
All those stops in 9 hours (9 am to 6 pm), three+ hours of which are in the car, don't sound like a fun day. Could you perhaps eliminate a stop or two? I recommend getting a Michelin paper map of the area. Seeing the "big picture" helps in planning a driving trip, at least for us. Plus, it makes a good souvenier if you trace your drives on the map!
I wish you luck. Provence is lovely and worth the time to really see and appreciate it.

When are you going? If during peak season, especially lavender time, you can kiss those drive times goodbye. It might work for you but it's much too tightly scheduled for me. I'd be a nervous wreck with the first traffic tie up.

When you plan such a tight itinerary, don't forget that the devil is in the details like those mentioned by Judy

You only take into account the travel times estimated by Google or other applications that are always too optimistic

Just for the first step, you estimate your arrival at 9:45 in Lourmarin. Do you know that the castle does not open before 10:30?

And where are you going to park the car in Lourmarin? At the castle parking lot? It's not possible near the Gaby cafe. Have you estimated the time to visit the castle, then the walking time to go from the castle to the cafe? then back to the car?

Same in Gordes, how do you estimate the time to find a parking space, choose a restaurant that is not too crowded, eat, then return to the car? Even if you do not hang around in the village, 1h30 is very optimistic.

The only part I find realistic is the last one: "Relax back at hotel." lol

Where are you planning to stay?

St Rémy de Provence is a good place to stay but not a great place to visit IMO, there is not a lot to see if you exclude Mausole & Glanum a little bit out of town.

Lourmarin, Bonnieux (good lunch stop), Gordes, Sénanque is OK for a 1-day tour of the Luberon.

Firstly, where are you staying? Secondly, yes it is too rushed. Stop and smell the roses. The villages are lovely and you will enjoy them more if you take your time to explore, stroll around, etc. You have less than 2 hours to visit 2 villages (Bonnieux and Rousillon) and then drive to Gordes. For example, we spent a couple of hours in Bonnieux walking uphill to see a church (I think) but also to enjoy the scenery and views. Each town deserves more than a 15 minute look-see. You don't leave yourself any time to see Gordes, only to have lunch there. And the drive times are slower than you think. And it could take a while to find a parking spot.

Thank you so much for the quick replies!

I tried to use AI (ChatGPT) to help plan, but it's definitely NOT as good as the Rick Steves community! :)

We are planning on May, here is our rough itinerary:
St. Jean Cap Ferrat (for 2 nights, we came last year and are bringing our mom this year) lots of walks, one morning in Old Nice, the Ephrussi de Rothschild, maybe Villefranche-sur-mer again.

Provence--staying at Chateau de Fonscolombe for 2 nights (half day travel, one full day, one morning before train to Paris)
Picking up the rental from Aix. Where should we spend the one day we have? Should we skip Provence altogether? The hotel in St. Jean is a little expensive so not sure we could add more days there...

Paris for 4 nights--this is our first trip to Paris so it will be all of the touristy spots, we're staying in St Germain Des Pres.

Travel Brooke!,
In planning your trip, many contributors to this forum recommend counting nights, not days. This allows for time traveling from location to location. e.g., you count 2 nights in St. Jean Cap Ferrat. That means one full day, and whatever part of a day you have on arrival there, and whatever part of a day you have before leaving after night two. I hope you can do what you plan in that time on the Riviera, without hurrying too much from place to place.
Good to see you are not planning things on your travel day from Nice to Provence. Have you sussed out the method and time involved in your travel from Nice to the Chateau? And the time it may take to get your rental car and the (possibly limited) hours the rental agency is open? Where are you picking up your rental? One point...Provence is a large area. In choosing where you want to go you are wise to keep to places close together, as you seem to have done. But, as I and others have said, try to trim down your places. One third of your day (at a minimum) is driving. The driver won't be able to enjoy the scenery with this schedule. I guess I am belaboring the point, but we have driven many times around France, and in Provence most of all, and your schedule really seems unmanageable. I believe Rick Steves has,or had, a separate book on Provence. Try to find it in the library or online. That will help you organize your day in a more manageable way. Best of luck!

To add......Four nights (three full days) in Paris will allow you to hit some (definitely not all) of the top tourist spots. Before going, check out your options and list them in order of importance for you to see. Choose from the list, estimate your time to spend there. Then arrange your sightseeing geographically to avoid backtracking. Next, be sure to reserve/purchase your entry ticket if that is required (e.g. the Louvre). Bonne chance!