driving in december
 

we are a family of 4 (all adults) asking for suggestions about traveling from Paris to Italy or Spain by car, but little scared about weather conditions....any help on this?

That's a lot of travel. How much time do you have? An itinerary would help.

At that time of year, not much to see on the road. Unless you want to stop specific places on the road, flying might be better. It depends on your itinerary and on how much time you have.

Keep in mind the limited hours of daylight. Also, driving west when the sun is getting low in the sky can be painful to the eyes.

If you hire a car in a country and drop it in another one usually there is a big fee to pay as somebody has to drive it back. This of course is not a winter issue.
I would check that the car has winter tires, in some countries may be compulsory, in other they are not. Winter tires are necessary in mountain areas.
It is difficult to give advices without an itinerary. Sometimes winter driving is absolutely normal, sometimes you have to cope with fog or snow or ice. It depends on local weather and you cannot tell in advance, sometimes you have to decide on the spot. Generally speaking, trains are the most reliable form of transportation - not 100% reliable anyway.

In France the roads are well maintained, and kept clear of snow if at all possible. There will be more of a risk in January or February, not so much in December, but you never know. There was a huge snowstorm last winter when people were stuck on the motorway for a long time, in the north of France. This was in February, though.

Winter tires are not mandatory in France, unless you travel on mountain roads.

As noted, insufficient information on which to give any relevant advice.

It sounds like the OP has never lived in a place where it can get cold in December, or they'd have an idea of what it is like to drive in December. It's the same as in much of the US, except the northern areas (or most southern, like Florida). There isn't much snow in December, it comes more in Jan-Feb. Aside from unusual snow storms, it's just somewhat cold, that's all, not a big deal if you are driving from Paris to Spain on the major big highways, which you can easily do, at least from Paris to the border of Spain. Then, you could easily drive on only major highways in Spain, also, depending where one was going (eg, E90 from Barcelona to Madrid).