I will be leaving the Relais du louvre for a day in the loire valley. Are there any convenient car rental locations near the hotel? what time to they open/close? Are they open every day? I will be driving to chateau du rochecotte.

None that I saw having stayed there.
You're going to drive in Paris? Brave soul!!
I've a 20 cent euro piece here at my desk that someone who knows these things suggests you either go to the airport or take a train to a city close to your chateau and THEN get your car.
My plan is to train Tours and pick up a car for the Loire trip I'm trying to plan.

Are you coming from the USA? If so, it's usually best to arrange a rental from an agency in the USA ahead of time (I use AutoEurope, a kind of consolidator). That said, it may be hard to arrange a one-day rental. On-the-spot rentals will be considerably higher priced. And I can't ever recall seeing a car rental outfit in that neighborhood, though I certainly haven't ever been looking for one.
I think Suzie's suggestion to take the train to Tours and pick up a car at the train station there is a better idea for a number of reasons.

Then the train to tours it is. Is the car rental location in the train station in tours? We will only need the car for one day. Driving through the Loire countryside is something we are definately looking forward to. What are the times of the car rental location in tours? We will be visiting the loire on a sunday.

Another Fodorite wrote all about it in a subject "Loire Valley Sunday"

can you try to find that thread? It doesn't look good for a 1 day trip in the Loire.

Are you flexible in your planning?

crcash:

There are probably a number of car rental agencies at the train station in Tours. You need to call Avis, Hertz, AutoEurope (1-800-223-5555) or whatever to see who's got the best deal. You'll get a voucher from whichever company you rent from telling you the location of the rental agency - but it's bound to be right at or near the train station.

I will have to check with the hotel to see how flexible we are. What is the nearest train station to the Relais du Louvre? I am very unfamiliar with Paris. How far away is the airport??

The entire duration of our trip is from Dec. 21-28. We will be arriving in Paris on the 21st. We planned on staying in Paris 21-25, spending the night in a chateau on the 26th, spending the night in paris on the 27th and departing on the 28th. I had hoped to leave paris early on the 26th for tours, pick up the car visit some chateaux that day. We then stay at rochecotte that night and visit some other chateaux the 27th and return the car late in the day. We would then catch a train back to paris late that evening. Does this itinerary need adjusting? Maybe we need to leave for tours on the 25th and stay an extra night in a chateau. Help!!!!

Your best bet might be to call AutoEurope for the car and see what they can offer.
We're picking up a car on a Sunday in October and found many locations in Paris and some train stations closed. We're picking up at Orly because of so few Sunday options. My guess is that the Sunday after Christmas may be even more difficult.

Trains to Tours leave from both the Gare Montparnasse and the Gare d'Austerlitz, both of which are in the southern part of Paris on the Left Bank. There are many trains daily, even on a Sunday (which would be your travel day). You can check train schedul;es at www.sncf.com. You could take a taxi or the métro to either station.

I was about to add that finding an open car rental place on a Sunday the day after Christmas might indeed be difficult. Check with AutoEurope and/or other agencies.

I'd also check and see if indeed any of the chateaux are open because its Christmas weekend...

I know that Avis is in the St Pierre des Corps station (outside Tours) but is not open until 3:00 on Sundays. I don't know if you would have any train/car rental difficulties by moving up one day, since that would be Christmas Day.

All the Chateaux I looked up are open the day after Christmas, and a couple are open Christmas (if website is to be believed).

Chambord is closed only Dec 25, otherwise open 9-4:45

Cheverny says "ouvert tous les jours de l'année" (open all days of the year)

Chenonceau " Castle is open every day of the year " From November 16th to January 31st. 9:00 a.m. - 4:30 p.m.

Chateau de Langeais - open daily except for Dec 25;
hours: 10 - 5:30