I don't know how to get from Le Somail to Narbonne but from Narbonne there are direct trains to Carcassonne that take 30-40 minutes. There are TER trains that cost 10.50€ and there are also TGV trains and TEOZ trains that will cost about 13€-14€ last minute and less if you book ahead. Not a tremendous savings even if you book ahead. There are also a few buses that take over an hour but you'll have enough train options daily to not need a bus.
You can get all the info you need at www.tgv-europe.com. Uncheck the box marked direct trains to see all options. The TER trains have no reservations so you can walk up and buy them on the spot. The other trains take reservations but I doubt they'd sell out so you can probably buy them on the spot as well. If the TGV site redirects you to the RailEurope site try entering another country, like Antarctica, as your ticket collection country.
It's bus 60 and here is the schedule:
However, there are very few daily buses between Le Somail and Narbonne and they are designed for school and commuter transport so a taxi may be your best option.
Thank you very much
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