traveling from London to South of France

I don't believe you can take the Eurostar directly... it may be possible with a change in Marseille or Avignon (or a change of station in Paris). I would check out direct flights, including budget carriers. Time-wise and cost wise it can be very cost effective, as it's a very competitive route. Then, take the TGV direct back to Paris.

I would fly instead . The Eurostar terminates in Paris. You can change in Brussels and catch the TGV in Brussels to Nice; try your search using https://www.trainline.eu/

The Eurostar actually does extend direct to Marseilles and Avignon, but the service is only up to five days a week (and pretty much 0 through last winter) As noted, you could connect through Brussels, as well. But a flight is definitely superior for this type of leg.

I would fly from London to Nice. You're talking about 8 hours of train rides to get between the two by rail.

I fly at least twice a year from London to Nice. I either go British Air from Heathrow or Gatwick to Nice with EasyJet. Quick flight & the Nice airport is small & easy to navigate into the city.

Be sure you don't fly into Nice on a major holiday. I arrived on May 1 this year, and there was no public transportation into town. There were very few taxis.

If you want to avoid flying, the best route is to take a train from Nice to Lille Europe (may have to change at Marseille or Lyon) and then take the Eurostar from Lille to London. This avoids having to cross central Paris by Metro or bus. Going on from Lille to Brussels is not necessary.