Traveling by train from Aix-en-Provence, France to Cologne

It is a long journey (about 7.5 hours), but surprisingly straightforward given the distance.
You can take a direct train from Aix-en-Provence TGV to Bruxelles Midi (that's in Brussels, Belgium), followed by a much shorter ride from Bruxelles Midi to Köln Hbf (Cologne main station).

It is also possible to go through Germany, with a direct train from Aix TGV to Mannheim and a connection there to Köln. It takes a bit longer, but could be cheaper.

Note that Aix-en-Provence TGV is ~30 minutes out of Aix-en-Provence by very frequent bus.

To search for long train journeys across Europe, the Deutsche Bahn (DB) website (bahn.com/en) is great for looking at train times.

I don’t know anything about the train to Cologne but as Balso said, the TGV station is almost 30 minutes outside of town. While the buses from the Gare Routière to the TGV station are super easy, I’d recommend a taxi on departure day.

Are you looking for the quickest way to get there? If so, I'd probably fly. I took a relatively fast and cheap flight with Air France to Paris Orly a few years ago for 50 euro. I'm sure similar is available from Avignon as well (possibly Aix). If you can get to Paris, you can connect anywhere.

I've taken high speed trains between Paris and Lyon, Paris and Reims, Paris and Bordeaux. They're fine but there's nothing particularly scenic about the ride and connecting through Paris means changing both trains and train stations.

connecting through Paris means changing both trains and train
stations.

Yes, but why would you connect in Paris? As balso mentioned, there is a direct TGV to Brussels and one to Mannheim/Frankfurt, so no need for a stop in Paris, unless you want to stop in Paris.

Yes, Brussels is better. Just making a comment, that changing in Paris requires a metro/taxi ride to a different train station, for anyone who hasn't trained in and out of Paris before.

Sometimes people prefer trains because they know they are making a much lesser environmental impact by taking the train versus flying. It's not always about the scenery (although it's usually a nice bonus, in my experience).