France

Lucky you! Have you looked at the Rick Steves suggested itinerary? It's a great starting point to get ideas.

https://www.ricksteves.com/europe/france/itinerary

By Rick Steves and Steve Smith So much to see, so little time. How to
choose? To help you get started, we've listed our top picks for where
to go in France, and our plan for your best three-week trip. Depending
on the length of your trip, and taking geographic proximity into
account, here are our recommended priorities: 3 days: Paris, maybe
Versailles 6 days, add: Normandy 8 days, add: Loire 11 days, add:
Dordogne, Carcassonne 16 days, add: Provence, Riviera 19 days, add:
Burgundy, Chamonix 22 days, add: Alsace, northern France 26 days, add:
Basque Country

Or his "At a glance" on the same page? Have fun!!

▲▲▲ Paris World capital of art, fashion, food, literature, and ideas,
offering historic monuments, grand boulevards, corner cafés, chic
boutiques, avant-garde architecture, and top-notch art galleries,
including the Louvre and Orsay. ▲▲▲ Normandy Pastoral mix of sweeping
coastlines, half-timbered towns, and intriguing cities, including
bustling Rouen (Gothic architecture, Joan of Arc sites), the cozy port
town of Honfleur, historic Bayeux (remarkable tapestry on the Battle
of Hastings), stirring D-Day sites and museums, and the almost surreal
island abbey of Mont St-Michel. ▲▲▲ Loire Picturesque towns (such as
Amboise and Chinon) and hundreds of castles and palaces, including
Chenonceaux (arcing across its river), the huge Château de Chambord,
Villandry (wonderful gardens), lavishly furnished Cheverny, and many
more. ▲▲▲ Dordogne Prehistoric caves, rock-sculpted villages, lazy
canoe rides past medieval castles, market towns such as
pedestrian-friendly Sarlat-la-Canéda, and nearby, for wine lovers,
St-Emilion. ▲▲▲ Provence Home to Arles (Van Gogh sights, evocative
Roman arena), Avignon (famous bridge and brooding Palace of the
Popes), the ancient Roman aqueduct of Pont du Gard, Orange (Roman
theater), the beautiful Côtes du Rhone wine road, and rock-top
villages such as Les Baux, Roussillon, and Vaison-la-Romaine. ▲▲▲
French Riviera A string of coastal resorts, including Nice (big city
with seafront promenade and art museums), romantic
Villefranche-sur-Mer, glitzy Monaco (casino), yacht-crazy Antibes
(silky-sandy beaches), intriguing inland villages (Vence and St.
Paul-de-Vence), and little hilltop Eze-le-Village, with marvelous
Mediterranean views. ▲▲ Near Paris Europe's grandest palace at
Versailles, the radiant cathedral of Chartres, and Monet's flowery
gardens at Giverny. ▲▲ French Alps Spectacular scenery featuring the
drop-dead gorgeous town of Annecy, Mont Blanc (the Alps' highest
peak), and the world-famous ski resort of Chamonix, with hikes galore
and lifts to stunning alpine views. ▲▲ Burgundy Aged blend of
vineyards and spirituality, with the compact town of Beaune
(world-famous vineyards), Fontenay (France's best-preserved medieval
abbey), Vézelay (magnificent Romanesque church), and the one-of-a-kind
medieval castle under construction at Guédelon. ▲▲ Alsace
Franco-Germanic region dotted with wine-road villages, starring
half-timbered Colmar and its world-class art, and high-powered
Strasbourg and its sensational cathedral.

Are you asking for an itinerary? How many are "we"? What are your interests? Cities? Villages? Beaches? Palaces? Vineyards? Museums? Fine food? Hiking? Mountains? Have you been to Europe before? Have you been to France before? France is a fairly large country with very diverse regions.

I would suggest a good place to start would be a guidebook on France, or a few travel videos to narrow down your choices. Then come back with questions about specific areas. But with only 10 days, don't try to spread yourself too thin. Pick a couple of places that most interest you, and come back with more specific questions.

We will be flying into Paris on 10/25 and renting a car.

OP will be coming from Italy, so jet lag is not an issue

https://community.ricksteves.com/travel-forum/italy/bellagio-2ff3dc31-d5f9-445e-bbea-0cb62d384ad5

job1156,
To clarify, you have 4-5 days in Paris at the end, plus 10 days for other places in France? Or is it 10 days total? First time in France and/or Paris?
If 10 days, NOT counting Paris, I would pick two areas, at most three, depending on which ones they are. If France is new to you, you could visit Alsace for 4 days (east of Paris), then down to Burgundy for 3 days and Lyon for 3 days. Alternatively, go west and southwest of Paris to Normandy and Brittany for 6 days and the Loire Valley for about 3 days, stopping in Giverny or Chartres on the way back to Paris. If your total trip is 10 days, I would just head for Alsace and spend 4-5 days there (with maybe a one day dip into Germany), or 4-5 days in Normandy and a bit of Brittany. More detailed suggestions about where to stop are easier to provide once you decide on a region. Try a guidebook for summaries of the different areas to see what appeals to you the most, and what provides the sights and activities you prefer. If the ones at your local library are older editions, it won't matter because the main sights everywhere haven't changed much over time.
Come back to us with info about your preferences in traveling and sightseeing.

10 days would be plenty for Normandie and Brittanyn (but the weather might not be the greatest on the coast in late October).

10 days is more than enough for Loire Valley and Chartres.

10 days is enough for Dordogne or Lot Valleys but I wouldn't drive straight there. I'd catch a train to Bordeaux or a flight south, then rent a car from there.

In late October, I think Provence would be ideal. Again, I'd start with an Air France or train to Avignon, then rent a car from there.