Bordeaux to Seville

According to the airport website Ryanair fly directly between the two cities, but only two days per week. (As always with budget airlines, be sure you understand the strictly-enforced luggage policies, and be aware that you will be expected to print out your own boarding passes.) If you want to use a flag carrier, Iberia fly to Madrid and you can get the high-speed AVE train from there.

thanks. Unfortunately we are locked in to a day and it isn't one of the ones Ryan flies there.

'What is the quickest least expensive way'
It is almost certainly impossible to have both anywhere in the world. Does your money really matter and are you time wealthy or do you want the quickest? If the first a combination of two buses will do it in about 20 hours.
My additional thought, not that I know much about flights, look to Bordeaux to Malaga and on to Seville by train.

As on your other question, Vueling airlines can be an option, but with a connection at Barcelona.