The train BCN-TLS is not an especially viable option, involving a change at Narbonne & probably a very late arrival (23:41) into Toulouse. In addition, you would be paying for 4 tickets, although there are often quite generous family concessions.

For speed and simplicity, driving on the autoroute via Narbonne is hard to beat. The ViaMichelin website reckons that it would take under 4 hours of driving this way (with about EUR 30 to pay in tolls). (This is their "Quickest Route".) Their "Recommended Route" goes near Andorra, and takes about an hour longer, and there are still some tolls to pay, such as for tunnels. (At that time of year, keep in mind that the Barcelona-Narbonne autoroute is one of Europe's busiest holiday routes and it's high season.)

These days, driving BCN-TLS via Andorra is much easier than it used to be. There's been a tunnel under the Cadi mountains (getting to Andorra from BCN) for quite a few years. Recently, however, they opened a new tunnel within Andorra which cuts out the 2400 m. (7800ft.) Envalira Pass, making the road into France quite a lot simpler. Andorra itself is a curious tax-free country, with the President of France and the local Spanish bishop as co-Princes. The population is around 65,000 but there are around 14 million visitors annually, who came mainly for the tax-free purchases and petrol (gas) that's about the cheapest in Europe. To be honest, and I have an apartment there, it's much nicer up in the mountains & away from the 14 million visitors. If you just want to do some shopping, I would suggest a shortish detour from the Michelin-recommended route into Pas de la Casa. Not very beautiful, but your kids might like the idea of going into a different country. You might even be able to get your passports stamped, but normally there are zero formalities, and generally no-one even stops as they drive in. (Not exactly DHS/CBP. )

A simple alternative that you might consider is simply flying into CDG on AA and driving or taking the train from Paris. The Michelin-recommended route gives 6.5 hours driving time from Roissy (CDG) to Toulouse. Again, there are tolls to pay, but you cover a lot of ground quickly. Generally, on the autoroute expect to divide the distances in Kilometres by 2 to get the no. of minutes it will take. (An average of 120 Km/h or 75mph.)

Have a good trip, whichever way you get there.