I see that you've listed your city-change days for both the city you're departing from and the city you're heading to. That can lead folks who only glance at the list to miscalculate the amount of time you'll have in each place. This is what you'll really have:
Paris: 2 full days (assuming Day 1 is when you land in Europe after the overnight flight) and some jetlagged hours on Day 1
Beaune: 1 full day and some hours on Day 4.
Lyon: 2 full days and some hours on Day 6.
Wildcard location: 1 full day and some hours on Day 9.
Marseille: 1 full day and some hours on Day 11 if you do not depart until Day 13.
I really liked Nice and Toulouse, and Narbonne seemed an attractive place when I spent a few hours there, but none of those are very convenient for a visit when you're starting from Lyon and later heading to Marseille. These are the travel times by rail (to which you of course have to add travel time between hotels and trains stations):
Lyon-Narbonne: 3 to 5 hours, then 2.5-3 hours from Narbonne to Marseille.
Lyon-Toulouse: 4 to 5 hours, then 4-5 hours from Toulouse to Marseille.
Lyon-Nice: 4.5 to 6.5 hours, then 2.5-3 hours from Nice to Marseille.
By comparison, you can get a TGV from Lyon direct to Marseille in 1 hr. 35 min.
I wouldn't bother spending an extra 5.5 to 8 hours on trains for not much more than one day in Nice. Most folks heading to Nice want to see quite a few other places along the Riviera and up in the hills. You wouldn't have time for that.
Toulouse is a nice city, but I'd want more than 1-1/2 days there, given the extra travel time of 6.5 to 8.5 hours travel time of 6.5 to 8.5 hours.
Logistically, Narbonne is the least-awkward option of the three, but it's also probably the least interesting.
I'd urge you to consider places not so far off the Lyon-Marseille route--places like Avignon (closest), Arles or Nimes.
I'm not a huge fan of Marseille, but there's enough to do there to occupy you for more than one day. A boat trip to the Calanques is a popular option, and a side trip to the cute town of Cassis (another origin point for boats to the Calanques) is also viable. So you could drop the non-specified destination and use all the post-Lyon time in Marseille and the surrounding area.
You can check train times here: https://www.sncf-connect.com/en-en/home/search/od