Advice wanted on strike situation

Conditions right now are not great for doing a lot of moving around between cities within France. They might change though after the next general strike day on March 23. You probably can wait a bit to see how things evolve. Unions are keeping the pressure on for the next few days for political reasons that will change after next Tuesday. It's unclear what their strategy will be after that.

Even during strikes, there's "minimum service" which usually means that it will be possible to get to your destination using the train tickets you already have. It might be on a replacement bus (that takes twice as long as the train) or at a totally different time or route than you had planned. Trains might be crowded and you could find yourself standing for at least part of the time. If you're patient and flexible, you will though eventually get to your destination. You might need to plan for "travel days" though rather than "travel mornings or evenings".

What are your plans for Spain? Since you have to return to Madrid anyway why not stay in Spain for those 13 days. There is so much to see and do I have the suspicion you may only be scratching the surface.

https://community.ricksteves.com/travel-forum/france/paris-trash-and-strikes-march-2023-travel

Everything in Montpellier was up and running today and should be fine. No transportation problems on your first leg. One or two Barcelona to Montpellier trains per day are still scheduled. Unfortunately, the 23rd is the next strike day, so if your train is cancelled, some of the others may be running. Trains have never been 100% cancelled.
Or, come the day before or day after as 2 TGV a day are listed. Do check your arrival station bc if it's Gare du Sud you need a shuttle bus to get to the center. Take a taxi, Bolt, or Uber if on strike. Gare St. Roch is downtown.

It's not clear if you are staying in these cities or riding through. However, Montpellier has been very calm...so far. Everything is running, festivals going on.

And for when you get to Paris, garbage pick up has started.

I would stick to your itinerary because the situation is likely to simmer down after a brief outburst when the vote of no-confidence is taken on Macron’s government likely on Monday. It is certain to
fail—just as the last ten against Macron have failed, and every one since 1962 has. When that happens, the new retirement age of 64 will become Law and—unpopular as it and Macron both may be—the opposition political parties have no viable alternative candidates for the presidency. The opposition political parties are disunited, with one already saying they will vote against the no-confidence vote on Macron’s government.
There will be nothing to be gained—in the short term anyway— by transit unions in continuing strikes to support a cause that has already been lost.

That doesn’t mean there won’t be any transit strikes or protests in France at a later date on another issue of importance.
For now, though, I think things in France are likely to get back to normal very soon.

I was there the week of March 5. And before I left there was a lot of "doom and gloom" on here about how the strike was going paralyze France and Paris would not be enjoyable etc....

Actual impact.. minimal.

10 days 6 cities?? IT's a check box tour IMHO Get off the train go "look I was here" and then leave... if that's what you want then it's great but it does mean that if a train in cancelled the house of cards could be in danger