one day from Paris to Giverny and then to ROEWN?! BEST advise!!!

This trip is definitely doable as a day trip from Paris. Take an early train from Paris to Vernon, the bus to Giverny meets the trains. If you're at Giverny when it opens you can see the gardens and ponds thoroughly and do a quick trip through the house and be back at the station in Vernon by 1:00 pm or earlier. Then train from Vernon to Rouen is only about 40 mins so you should be there before 2:00 pm, which if you're there in summer and have long daylight will give you until about 7:00 or 8:00 to explore. Train from Rouen back to Paris is about 1 hr 15 mins so you can be back in Paris somewhere between 8:00-10:00 pm.

We thought of doing this but ended up not as we wanted to spend more time at Giverny. But Rouen has a tiny walkable town center within an easy stroll from the train station so you could easily visit the major churches and wander around the town in a few hours and make this part of a day trip to Giverny. I'd get to Giverny just before it opens with tickets purchased ahead so no line to wait in. You would need a ticket to Vernon and then another ticket from Vernon to Rouen and then of course a return ticket Rouen/Paris. Have those all in hand before the trip. I advise getting them a day ahead at least as there can be long lines to buy tickets at St. Lazare. We missed our train to Giverny because I had to wait over an hour. Locals use the machines except for complicated schedules so the line moves slowly. American credit cards if you are American don't work in the machines. If you have a European card then you could use the machines.

Here is our visit to Giverny: https://janettravels.wordpress.com/2010/05/25/not-so-secret-garden-giverny/

Rouen is delightful and entirely different from Paris architecture.