Once you factor in the time it takes to get to the airport, the TGV train is certainly the fastest way to get across the country. It’s also the most expensive. Taking a slower train is can be somewhat cheaper but it may require several changes en route. Budget flights are only worth your time if they greatly outstrip the cost of train tickets or you’re headed to somewhere like Corsica that’s not easy to otherwise reach by public transport. Just be sure to factor in cost of getting to/from the airport into your calculations along with any baggage charges that might apply. For travelers with more time on their hands than money, the bus is certainly another option. There are even some overnight services available.