From Paris CDG airport: direct TGV high speed train (the train station is directly within Terminal 2, so a few minutes walk if you arrive at one of those terminals, or a short people-mover hop if you arrive at Terminal 1). Takes about 3.5 to 4 hours to Marseille, with about 10 trains per day.
You'll have the choice between regular "TGV Inoui" trains or cheaper (but less frequent) "Ouigo" trains. Note that for Inoui trains, reservations are not open yet for the second week of January, they usually open about 2 months in advance. If you want a reference, don't look at prices from mid-December to early January, as they are a lot higher than usual due to holidays. For Ouigo trains, you'll have to pay extra for luggage.
You also have the option to go into Paris proper and take a TGV from there. Even more trains and a slightly shorter trip (3 to 3.5 hours) but unless you want/need to spend some time in Paris it's probably not worth the hassle. Likewise there are trains from Marne-la-Vallée, which is code for "Eurodisney".
There are also Air France flights fro CDG to Marseille. When looking up flights, make sure you pick CDG airport, not "Paris all airports", there are more flights from Orly airport (ORY), but that airport is on the other side of Paris, so it'll take you well above an hour to get from CDG to ORY (unless of course you somehow arrive in ORY instead of CDG, see below).
Finally, there's the option of taking a bus from Flixbus, but that takes over 11 hours, there's only one direct bus a day, and you can get cheaper Ouigo fares (though this may depend on the exact train you want and how much luggage you have). There are more options from other bus terminals in Paris and around, but again, very very long, and in some cases quite inconvenient to get there.
Unlikely, but if you arrive at Paris Orly airport (ORY), it's a bit more complex, you'll probably need to travel to downtown Paris to take a TGV from Paris Gare de Lyon station. You can take a taxi (fixed fee from the airport) or public transport (quite a few options, but they all involve at least 2 changes, and it takes about an hour).
There are also quite a few flights from Orly to Marseille.
Another option is to go to Massy TGV train station (take Orlyval then RER B to get there, takes about half an hour) where there are a few direct trains to Marseille (about 4 hours, 3 trains a day) and a few more with a change (in Marne-la-Vallée or Lyon, 4 to 5 hours), though I would still recommend going downtown.
A final option is to go to Marne-la-Vallée train station (Eurodisney), but it's not really easy to get there from Orly, so you're better off departing from Gare de Lyon (the most obvious route to get to Marne-la-Vallée goes through Gare de Lyon anyway!).
From Lyon Airport: direct TGV high-speed train (the train station is just opposite the terminal). Takes about 1.5 hours, but choice is limited (3 direct trains a day).
Alternatively, you can go into town using the "Rhônexpress" tram which bring you directly to Lyon Part-Dieu train station (about 30 minutes). From there trains to Marseille take about 1h40-1h50, and there's a lot more choice (over 15 trains a day). Note that some of the cheaper "Ouigo" trains depart from Lyon-Perrache which is another train station in Lyon.
From Lyon-Perrache you can also take Flixbus, about 4 hours, 3 trips a day, but two of them through the night.
On a map Nice looks like it's a lot closer, but given the local geography and lack of a high-speed train link, it actually takes quite a bit longer: 2.5 to 3 hours to Marseille. And that's from the main train station (Nice-Ville), so you need to add time to get there from the airport (about 30-45 minutes).
There's another train station closer to the airport (Nice Saint Augustin, about 15 minutes from the airport), but there are less trains departing from there.
You can also take a bus (Flixbus), with 4 buses a day, taking between 2h30 and 4h10 (!). Buses from Nice depart at the airport.
Funnily enough, Geneva airport may be an option as well, with quite a few options by TGV high speed train around 4 hours. You'll have to take a quick hop from Geneve airport train station (right next to the main terminal) to Geneva main station (Genève-Cornavin) to catch the TGV there. Pay attention to local Covid regulations which may be different, though.
So, as you can see, quite a few options, though with a variety of pros and cons:
- The most obvious choice is probably CDG, as you'll probably get the most options (and the cheaper ones) to get there, and you have direct trains right from the airport. The main drawback is that it takes 3.5 to 4 hours, which after a long flight or combination of flights may not be the most entertaining.
- LYS is a lot closer but direct options are more limited, so unless your timings are great you'll have to go downtown, which will make the trip longer and less convenient.
- NCE is geographically closer but not very convenient (longer train ride + need to get to the train station first). But you can get a very nice view when landing!
Don't forget to take any possible disruptions into account. Pay a little bit extra to get flexible tickets and be sure to have convenient alternatives. If you book enough in advance you can also often get first class for not a lot more.
Book as early as possible (i.e. as soon a reservations open) to get the best prices. Depending on your dates of travel and other conditions, you may be eligible for discount travel cards (though some have extremely unclear rules) which may cost less than the discount you get (though I don't know if they're really practical to get from abroad).
The fun part is that due to some marketing gimmick, the main site for booking trains in France is oui.sncf, not sncf.com.
Finally, to travel on any long-distance public transport (train, bus or plane) you'll need to have proof of vaccination or of a recent negative test (the so-called "Pass sanitaire", which is also required for access to restaurants, bars, museums, cinemas, and many more public places).
For French and EU passenger that's easy with the EU Covid digital certificate. For non-EU foreigners who have been vaccinated, there was a procedure to convert foreign certificates into a valid pass sanitaire, but that seems to no longer be the case, so it will probably revert back to manual inspection of a paper certificate. You should also be able to get a test done locally and get a QR Code valid for 72 hours.
You'll have to wear a surgical mask during on board all trains and aircraft as well as inside all train stations and airports. Make sure you have a few replacement masks at hand to last the whole trip.