If you have the time and patience for it, you can do it. Mind that France is one of the most annoying Eurail/Interrail countries, with lots of mandatory reservations and rather inflexible booking, and infrequent connections.

To travel validly with TGV InOui, you need a seat reservation + a valid pass. You can check shortly before if there’s any availability at the ticket office or online (https://travel.b-europe.com/Eurail-GE/en/booking-tgv#TravelWish → only for domestic journeys in France).

If not available, the TERs are a much slower alternative, usually not that frequent. But you can get somewhere, often via more interesting routes than the rather boring high-speed lines. Plenty of smaller towns and villages to discover that way, but you need time.

Early december on weekdays it’s probably going to be okay to find free places on most trains. (Fridays and Sundays might be a bit harder).

If you plan to travel around Christmas: forget it to hope on as you go. Reserve asap, as demand will be huge.

If you plan international TGV’s (e.g. to/From Germany), best reserve in advance or use the workarounds.

But mention your (rough) travel plans in order to help you advise for the workarounds for crossing borders. Community advice can save you a lot when crossing the Belgian, German or Swiss borders from/into France ;)

To be clear, you can’t travel on a TGV without a reservation, and you’d be liable to a fine. It doesn’t matter how full the trains are.

As above, there are often routes you can take without reservation, but these are often slow. You can find routes without reservation in the Eurail planner.

As @BrendanDB suggests, if you mention your plans, people can advice reservation-free itineraries (as well as advising when it’s not worth the effort)

So we plan to land in Paris on 7 th December and want to take a train to strasbourg from the airport itself … somehow I can see only TGV … I cannot see any regular trains that can be hopped upon without reservation… 

can you pls help me with a link that could show me trains that do not require reservations 

so our plan is to buy the France rail pass … 4 days in a month for 190 usd per person 

we could go to and fro …  paris - Strasbourg - Paris 

that almost covers the charge of buying a return ticket 

additionally with this pass we can explore towns around Strasbourg stress free with this pass 

but when it comes to reservations we end up spending almost 100 usd for 2 only on reservations which we think is a bit steep 

We are visiting France only to experience the spirit of Christmas 

so it’s just paris -Strasbourg…. Explore the towns around for 3 days and back to Paris … spend 3 to 4 nights and back to india

we will be on a budgeted trip so want to make the most for our buck 

would really appreciate

There are only 2 direct non-reservation TER trains per day Paris - Strasbourg.

Currently they are: Weekdays 07.35 - 12.37 and 16.35 - 21.21, Saturdays 0835 - 13.19, Sundays 16.35 - 21.42

There are also a few other possibilities requiring connections.

As you can see the journey times are much longer than the 2 hours the TGVs take.

This is not unusual for France, in general the TGV replaced the former express trains on the old lines and if the lines were retained at all only a skeleton service is now provided.

Regional routes can have reasonably frequent trains but long distance is by and large only on reservation required TGV services. With the high reservation fees France is one of the poorer value countries to use Eurail especially in the manner you are planning.

You won’t find any direct trains Paris CDG - Strasbourg without reservations.

If you go into Paris first by RER or bus (you have to pay for this) then you can get the TER all the way to Strasbourg. No reservation needed on the TER, but it takes 4.5 hours and there aren’t many options per day.

The reservation fee for the direct TGV from the airport is €10 or €20, and there are some left at €10 on 7 December. (When the limited number of €10 reservations sell out, it goes up to €20).

So unfortunately this isn’t really a route where you can save much by taking the slow trains.

Great !!! Thank you so much for all the answers !!! Now I’m pretty clear in my head !!! 
10 euro isn’t that much 

I think will go in for the France rail pass 4 days in a month 

and take the reserved seats 

to and fro Paris 

will cost me Approx 440 usd ( almost the price of buying a return ticket ) 

All The other travel We do would be a bonus 

Before you commit, check the price for your preferred trains in both directions here:

https://travel.b-europe.com/Eurail-GE/en/booking-tgv#TravelWish

It’s €10 for one of the morning trains and several of the afternoon trains on the 7th.