9 Nights in France - Paris + ???

...keeping Paris as our home base and doing day trips.

That would be my suggestion. Unless I misunderstood, your nine nights will only give you eight full days. The arrival day may not count due to possible travel delays and jet lag. One could spend the entire time In Paris and only scratch the surface. But there are many day trips you can take. One of our favorites is Reims. Beautiful catherdral, Museum of the Surrender, and many champange houses to visit. You can get there easily and quickly by train.

If you like cathedrals, Chartres. If you like chateaus, rent a car and drive to the Loire. Be sure to pickup and drop off the car somewhere outside of Paris. You can buy a book on Amazon that describes possible day trips from Paris.

I would spend all the time in Paris with one or two-at the most-day trips. I just spent two weeks in Paris-there is SO much to see and do and not just museums. As a side note, I wasn’t prepared to enjoy Paris as much as I did. So much so, I want to return.
Of our 14 full days, we only took one day trip to Chartres, which is well worth seeing. If the labyrinth in the cathedral is open to walk (Fridays only, 10-5) that is special. It may be by the end of March.
If we had visited in a better season for Giverny, we would have added that as a day trip too. Unfortunately, it was rainy for most of our time and in late October, I wasn’t sure the gardens would be that nice. We were told however, that they are worth seeing anytime of the year.
Both Chartres and Giverny are easily accessible from Paris.

amandatravelforum,
Giverny may have early spring flowers in bloom when you are there. We were there in April 2017 and the tulips were abundant and eye-popping! You could visit Giverny and still return to Paris for an evening cruise on the Seine with Vedettes or Bateaux Mouches. Other day trips could be Chartres one day, and a chateau, Versailles OR Vaux le Vicomte, another day. But you could spend every minute in Paris and still not see everything on offer. Besides, you will want some down time to relax at a cafe or in a park and watch the world go by, Paris-style, as you sip on a coffee or aperitif! With only 9 nights (8 days), I would pick no more than one day trip outside Paris. It took me many trips to France before I got to Giverny, and I would put that lower on my list, especially since it is early in the year. Spend all your time in the City of Lights and maybe do just one trip outside Paris....Chartres OR a chateau.
You all will fall in love with Paris! Amusez-vous bien!

I'm with the others about staying in Paris and taking day trips. But if you want to spend a night somewhere else, just turn a day trip into an overnight. Chartres or Reims would be good choices, both easily reached by train, but on opposite sides of Paris, so choose one or the other. This book offers other options -- but it's 11 years old so check current timetables.

Pretty sure Giverny doesn't open till April.

If you decide to do another destination outside Paris then do it first and finish in Paris for the trip home. You don't want to waste a prime day on the logistics of returning to Paris for your flight the next day.

The weather is likely to be rainy and chilly which suggests Paris with day trips when the weather looks up. There are literally a couple dozen great day trips within an hour or so of Paris --Reims, Chartres, Versailles, Auvers sur Oise, Senlis -- are some obvious ones, but there are many others.

Spend 5-6 nights in Paris with a day trip to Versailles and then take the train to Colmar for 3-4 nights with day trips to a few Route du Vin villages.

I highly recommend Normandie. France is an incrediblly diverse country with so many unique languages and regions. Normandy has great connectivity to Paris and is another world. Half timbered buildings, calvados and cheese tasting, beautiful cliffs of Etretat, beautiful Rouen Dauville and Honfleur, You have Dday and many things to do. If you cant spend a few days there then just go for a day trip, more ideas here: https://theparisshortlist.com/best-day-trips-from-paris/

You can’t go wrong spending all your time in Paris unless you turn out to be one of those people who are not charmed by Paris. Something to consider.

If it were me, I’d spend three nights in Normandy and the rest in Paris. I love history, especially WWII history, but I know people who are not into history who were moved by the D-Day sights and cemeteries. Even without the WWII sights, Normandy is a charming area.

I second Chartres as a wonderful day trip from Paris.

I would offer advice counter to most here. If it were me, I would short yourself on Paris and hit 2 other cities nearby. Yep - you’ll miss a bunch of Paris, but France has much to offer. Also since Paris is a relatively inexpensive hub, there’s a good chance you’ll be back so leave yourself wanting more. Lyon and Bordeaux are only a 2-2.5hr train ride (I’ve never been to either but they are on my list). I honestly would not spend more than 3-4 nights in any city on a 9 night vacation. Keep the transfers short or make your travel days, sightseeing days (eg train to Versailles, then train to Chartres and overnight there).