Trains to Giverny

Yes.I am getting 43.50 EUR for most trains

Bastille Day?

If Tuesday is Bastille Day, then many / most French people will take off the Monday as well. This even has a name: faire le pont, making a bridge.

Lavandula

Normally, it isn't necessary to make reservations for that train. But being a holiday I would in this case. For what it is worth, the French do not refer to it as "Bastille Day." That is more a US/UK thing. They officially call it "La Fête nationale" (National Holiday), or simply "le quatorze Juillet" (i.e., July 14th). I personally call it my birthday!

There are engineering works on that day.

You may not have realized since the notice only pops up on the French version of oui.sncf, although if you look closely at the itineraries proposed for July 13, you'll notice they are much longer than usual (over 2 hours) and all with 1 connection -- you have to go all the way out to Rouen, then backtrack to Vernon-Giverny.

Attention Info travaux trains Nomad

Des travaux sont prévus du 11 au 14 juillet sur votre ligne impactant fortement la fréquence et le temps de parcours. Pour votre confort nous vous invitons à réserver votre voyage en dehors de ces dates.

In English (Nomad is the branding for regional trains in Normandy):

Important: Nomad Train Service Updates

Engineering works are scheduled on your line from July 11 to 14, significantly impacting service frequency and journey times. For your convenience, we recommend booking your trip outside of these dates.

Thanks all. Have been 4x but never in the summer. I am not willing to spend $80 on the train, plus 2-3 hours on the train. So will need to come back another time. But thanks for clarifying I am not going crazy.

The summer isn't the best time to go anyway, if you've already seen spring and early fall, have no regrets!
If you really want to go, you could use a tour with transport, though.