Another option to consider is the train. You could take the Eurostar from London (I'll leave the best way to get from LHR to St Pancreas to the London specialists) to Paris-Gare du Nord (~2h20.) From there, hop on the metro line 4 to the Gare Montparnasse (~20mn) and take another high speed train to Nantes (~2 hours)
If you book your train tickets early enough or come across a sale, this might be a good option for you. Especially for the TGV (French high speed train), prices can be all over the map depending on booking date, travel date, types of passengers (under 12, under 25, over 65...)