My husband and I will be traveling to France, Germany, Italy, and Spain and will be starting in France.

We were thinking of staying in Paris for 3-4 nights then rent a car to Champagne, Chambord, Bordeaux, Burgundy, Cotes du Rhone, French Riviera. I know that's ambitious for 15 nights total so any advice on what to skip and what to make a priority would greatly be appreciated! We love food and wine along with exploring the historical/cultural sites!

Also was wondering since we are also going to Italy would it make sense to make our way to French Riviera from there itself and continue onto Spain from there? Or is it better to stay in one country and make a loop then move on to the other countries?

Too many destinations and too much driving for 15 days.

I would suggest:

Paris - Champagne - Bourgogne - Côte du Rhone - Côte d'Azur - Italy (drop the car in France, cross the border by train and rent again in Italy).

Let's take a look to the "Route des Vins de Provence" on http://routedesvinsdeprovence.com/.
Maybe you'll pick some ideas of steps between the Cotes du Rhone and French Riviera.
In the Vaucluse region, Chateauneuf-du-Pape, Gigondas, Vacqueyras and Beaumes-de-Venise are some of the most well-known wine appellations.

I am not following your narrative. Are you planning 15 days in France and then on to Spain or Italy or is 15 days the totality of your vacation? If you only have 15 days total, you can cut your itinerary in half and still have too many places in too little time. What you are purposing would take at least 4 to 5 weeks and be hurried at that.

Even if 15 days is allocated all within France, you´re crisscrossing the entire country. Starting in Paris, I might suggest Burgundy, the Loire Valley, Dordogne, Languedoc and finally Provence. If you are planning on Spain, you would go there from Languedoc and return to France to continue eastward through Provence onto Italy.

Without knowing what you really have in mind, it would be difficult to help you much or make meaningful suggestions.

I would add Belgium.

I am also not sure of your intentions. How much total time do you have for your entire trip? What time of year are we talking about? What parts of Europe have you visited in the past?

I too am confused. I think you first need to look at a map and plot your route from country to country before you start zeroing in on which places in which countries. At any rate, even if you do have 15 days for France, you'll need to cut down the destinations there. If you're headed to Spain after France, go to the Loire, then Bordeaux, down the Atlantic coast, and then into Spain. If you're headed to Italy next, forget the Atlantic coast and Bordeaux and start off with Champagne and work your way southeast.