Cool, it worked!

De Gaulle is eliminated (see screenshot)! I only lost one Keshik against only a few archers, warriors and a single chariot. There was no metal in his territory.
He had 3 cities and I kept Orleans and Paris (they both had a Granary) but razed Lyons which had no building at all and I believe it was too far away and too close to Willem's borders (see the city ruins in the upper right corner 1N of incense, that was Lyons; the orange corner on the right edge is Willem). I don't know if razing was the right decision here. But I think expanding to North and West is the better direction. I also captured 2 workers from De Gaulle.
If a city has Food, you should keep it. You don't have to worry so much about maintenance, because you're playing on a low difficulty, and even on the higher difficulties, one can counter higher distance maintenance very well. As I wrote, as long as you got Currency and a foreign Traderoute, a city is able to sustain itself.
I tried that but somehow messed it up and needed a lot more turns in the end (also I built more Keshiks to be on the safe side). I got Math during the Keshiks production, so some chops had 20 and some 30 hammers. Will try your strategy again next time.
To pull of rushes like
elitetroops describes, you need to micro your cities, so you need to assign the citizens manually, and you have to pay high attention to production every round. CIV is a game, in which good micro is very important, so better you learn it now rather than later.
You need to disable the city-governor on the lower right bottom of the city-screen, and you should enable the log in the upper left corner on the main screen. Every time a city grows, you go to that city and check if it's citizens are working the best tiles. The city govenor does horrible things, like i. e. not working the Food, when a city is unhappy, so it's really best to not use him.
Hm, now I have 4 cities and basically build libraries everywhere (partially with chopping). (In the capital the library is finished.) I thought I must get culture to push the borders soon - especially of the new French cities. Is that the wrong way? And if I don't build libraries what else would I build? Granaries are already in all cities and the only other options (regarding buildings, not units) are Barracks, Ger, Walls, Aqueduct and Monument.
Monuments are a lot cheaper for Borderpops than libraries, and Religion also gives you

, if it's your state Religion or if you run no Religion at all, like now. Better get more cities, don't stop at 4, think 20 when you have 10 and 40 when you have 20. As I wrote, in CIV, more cities are basically always good.
Some new questions:
_ I have just traded techs with Willem: He gave me Mysticism, Fishing and Iron Working for Horseback Riding. He was also willing to take Math from me for the same 3 techs. What is the better tech to trade? I thought, Math is the more advanced tech, so giving him "only" HBR is the better deal.
Better give him Maths, with HBR, he gets better units, and you may want to conquer him directly afterwards, because troops that stand around are a worthless investment.
_ Asoka has spread Buddhism in 3 of my 4 cities. Should I convert? At the moment I don't have a state religion and I think getting the happiness and culture bonus is worth it to convert, right?
You get the

also without having a State Religion. The

is nice though, and as Asoka probably is also buddhist and is on "Missionary Strategy" (building less units and spreading Religion) , it's likely that most of your neighbours will become buddhist, so yes. Try to adopt the religion of your neighbours, to gain diplomacy bonuses.
_ What are the next techs to research? I'm working on Currency at the moment and thought I will proceed with Calendar after that to be able to build plantations (especially for the multiple silk tiles next to Paris).
_ Should I aim for a second Keshik rush? I'm more inclined to develop my territory peacefully for the next centuries, especially because I have A LOT of room to expand without conflict at the moment. Willem in the east region is the closest and even he is not really close. The other leaders seem to be mainly in the north and are still rather far away (Pericles is next closest).
Currency is a good choice. You can also think about researching Construction, and conquering the whole map with Catapults + Elephants though. To get Elephants, you must settle an Ivory resource and connect it, Elephants are the superior unit of the classical age and last until the enemy has Rifles. Code of Laws afterwards would be good, because it unlocks Civil Service, which multiplies the

and the

of your capital if you switch to Bureacracy (
elitetroops already made a post about that) .
Calendar is often teched by the AI, so it's no desirable choice. Should the AIs be so slow in your game though, that they aren't able to contribute anything, which depends on how well you play, you should self-tech Calendar probably, but more after CS, to better sustain your growing army by having more

.
Other choice would be to peacefully expand ("REX") to all available land as long as there's Food, but simply killing the AIs is cheaper and easier, but you decide, if you i. e. want to learn the basics of a Space Race victory, REXing to all available land makes sense, if you want to go for Culture, you need a completely different tech-path than the one I suggested, if you want to go for Diplomacy or the Apostolic Palace, you also need a different tech path and be nice to the AIs so they become your friends. Domination / Conquest is usually the cheapest, but most fun type of victory, Space Races requires the most skill and lets you play the game through completely, Culture needs good calculations and diplomacy takes a little longer than Domination / Conquest, but it's also very easy and very cheap. AP is even cheaper than Domination / Conquest, and is not regarded as a real victory by the most players, because it can be achieved at 2000 BC and requires a totally unique style of play.