From Marseille Provence airport take the train to Vitrolles Airport (10 minutes), then a train to Narbonne.
Train timetable : www.tgv-europe.com

Some confusion here, thanks to the convoluted marketing history of the Marseille airport and snarled SNCF/TGV logic.
The Provence name and Vitrolles name describe the same airport outside Marseille. The TGV Internet site will accept "Marseille Provence Aeroport" for its search function. The 5-minute shuttle is a bus connection to the small train stop. This can all be seen at http://www.marseille-airport.com/access-car-parks/access/trains
To ride the shuttle you must have a train ticket, which can only be bought at ticket machines outside the terminal, and only using a card with a chip. No attendant, no cash. I presume that a ticket bought over the Internet will work too but I didn't have one three years ago and had to take an expensive ride into Marseille to get a connection.
Maybe SNCF/TGV can tell you if arrangements have changed since then.
Your estimated time of arrival raises another complication. The last direct train to Narbonne from the airport leaves just after 7 p.m. so you probably won't be able to collect your bags and catch it.
However, there is a Narbonne train from the nearby Aix TGV station at 10:20 p.m. You might be able to take the TGV bus shuttle from the airport to catch it. Here are the details; remember that you are going to the TGV station and not Aix Centre http://www.marseille-airport.com/access-car-parks/access/shuttle-buses/aix-en-provence
I am not adept enough to manipulate the tgv-europe site to ticket the airport-Aix-Narbonne route as one itinerary but you can buy the shuttle ticket and the Aix-Narbonne ticket separately on the site.
Another pessimistic thought: Are you carrying bikes? They might require special arrangements.
If so, I think you should try e-mailing or phoning SNCF/TGV to sort it all out.

I had that problem once in MRS, I couldn't use that shuttle or it didn't have very good times, anyway, I don't recall the details but I couldn't do it. I just took a bus but I was going into town to the gare, and that was probably just as easy, anyway (train vs. bus), or easier. Vitrolles is just the name of the place the MRS airport is located. Part of the problem is that is only a TER station, I believe.

This is going to be difficult so late at night, but I think the best option could be to take the train from the airport to Avignon centre at 20:07-21:35 (TER 79636), then there is a train from Avignon centre to Narbonne at 21:40-23:59. That was the best option I could see. Both allow bicycles.

I didn't have any problem getting the SNCF website to quote a ticket for that route, around 40 euro. YOu just have to put in Vitrolles airport in the "to" box, and Narbonne as the destination and then check that you want the trajet to go through Avignon.

I don't use tgv-europe, I use www.voyages-sncf.com but I suppose it should be the same thing, in theory.

If you can get the 19:28 train from the airport to Narbonne, that would be great.