Hi Brisey good to hear from you
For the route you are taking I don't believe you will need them. It's only a legal requirement when road signs say so. It would be a different matter if you we're going up and over, rather than around the Pyrenees.
There is a useful list of various countries' requirements here
http://www.caravanclub.co.uk/media/7707033/winter_equipment_requirements.pdf but the bit that concerns your trip is
"It is not a legal requirement to carry snow chains or have winter tyres fitted in France, however if the international road signage for snow chains is displayed it is then a legal requirement to use them."
Have a great trip and pop in if you are passing :thumbs: