The short answer is YES, there have been significant disruptions to the TGV service for the past several months. Whether you will be affected by this is anyone's guess at this point. Pay attention to the SNCF website starting a week before you go. In most cases, the cancellations are "scheduled" by the strikers, and you will have at least a little warning. On most strike days, they have not cancelled all of the trains, just some of them. In a worst case scenario, you may have to reschedule your travel to another day, or book a flight to Biarritz instead of using the train. In the best case scenario, your travel is unaffected. You will not know until just before you go.
Not to worry. You will make it to SJPP. It just might be a little bit complicated if you find your train cancelled have to find another train at another time, or find an alternate way to get down south. Once you get to Paris, walk into the SNCF office at the airport, and they will reschedule you if it becomes necessary. The good news is that you seem to have a little sway space in your plan - well done! With luck, it will all go according to plan. Without luck, you have an unplanned night in Paris, and take the train straight to SJPP the next day.