France's leader is actually De Gaulle.
From the options to continue that elitetroops suggested I decided now to go for Horseback Riding and then try to take out De Gaulle. He already expanded into my direction with his second city Orleans (which is exactly on my former X4 tile). I have started another game with random leader and got Huayna Capac. In that game I already have the Oracle and want to try the more economic path there.
How unfortunate, that you started a new game, De Gaulle founded that city to your advantage, and you should have been happy about it, but ok. Try to play slowly this time, and play a different game to have fun in the time that you're waiting for advice. Once you do this, you'll be catapulted to Monarch at least.
My current status is now (screenshot attached):
_ 2 cities
_ 3 workers, 2 warriors, 1 scout (unfortunately a lion killed the other scout)
_ The capital has a Granary (whipped) and I'm building a library right now
_ The second city is building a Granary
_ 5 cottages (all being worked, partially by the "helper city"), all in the capital's BFC. The 6th cottage is in work right now (on a flood plain), but it won't be in the capital's BFC. Only the second city can work it. I'm not sure if I should have prefered to build a farm for the helper city. It doesn't have much food, so I think I'll need a farm soon.
_ Quarry is built and Marble is hooked up to the cities
_ Horses have a pasture and are hooked up to the cities
_ The scout discovered 3 fish tiles at the coast
_ 1 turn to go for Horseback Riding
_ I have open borders with De Gaulle, Willem, Pericles and Shaka
_ I will move the scout now from the coast to France to spy there a bit (Orleans has only one warrior, Paris is hidden)
3 Workers for 2 cities are too much, try to think heavily about your Worker actions, and only do the most necessary stuff. It's not too bad, if your cities work some unimproved tiles in the very beginning, it's only bad if you got lots of unimproved tiles later. 1 Worker + 1 extra for the capital is the rule of the thumb, but initially, you can very well simply improve 4 tiles of your capital with your first Worker, and then let him hop over to city 2. Your capital shouldn't grow larger than size 4 very early, so you can get along with those 4 tiles 'til, let's say, 2000 BC. 'til then, you can get 3 cities while having 1 Worker at least, and every city is gonna have 2-4 improved tiles, if you i. e. don't build any roads (you don't need roads early, except your city is very near, and you wanna establish a Traderoute because it has no River-connection. Cities that are further away don't deserve a road connection early, you'll just have to live with the city having no Traderoute until you get Sailing and Rivers that aren't in your territory will connect it. )
It's also too early to build a Library yet. You should expand to 3 cities, before you build one. The reason is, that Libraries are very expensive buildings, especially in the beginning. Ofc a Library is great to have in the capital because it allows hiring Scientists to create a Great Scientist and becaue it pushes research, but expanding to 3 cities is even more important. Once you've got those, your other cities can take over production of Settlers and Workers so you can keep expanding, while you divert your capital to building the Library, to give you the things I mentioned.
If your capital is already size 5, you let it grow too much, and produced too few Settlers. Size 3-4 is perfect for up until the 3rd city, sometimes it's even advisable to stay that small a little longer, but expanding always has the greatest priority in CIV. Cities are power, and every city contributes to your empire, once you got Currency and a Traderoute (connection between the city and another city, preferably a foreign one) . The expert players in these forums are heavily trying to get the most cities that the game allows for at every time. The only thing when it's not worth to expand, is, when expanding would get more expensive than a Settler, those are super-rare cases though, where one would needs extreme military to conquer an opponent. If you play well, that should never happen.
Fishes are great sources of Food, but building Workboats slows down the improvement of a city very much. You should always try to get the landlocked cities first because of this. If you can get a city that has Corn or Pigs, forget about the 3 Fishes city for a moment, if an AI builds it for you, great, then you conquer it, if not, found it later, when your empire's capacity is greater.
I have some questions again:
_ The capital has one sad face (one citizen refuses to work). Somehow I have this problem in almost all games and don't know how to deal with it. I don't see additional happiness I could get and there is one "we cannot forget your cruelty..." from whipping the Granary. In addition the capital grows faster than I want (I have already assigned the overlapping grassland cottages to the capital and flood plain cottages to the helper city and work the quarry instead of the corn and wheat tiles to slow down the capital's growth). What can I do? Just ignore it and wait for happiness resources (or maybe religion)? Or should I employ a citizen as a scientist or so...?
Simply build Settlers and Workers in the beginning and keep your city at size 3-4, until you got more Happiness. Cities consume all surplus

when you build those two units, so they cannot grow into

.
So, next turn I could start to build Keshiks. Should I do that immediately in the capital (stopping the Library for now)? Or should I build a Ger (the Mongolic Stable) first? And how many Keshiks should I build? Or maybe found a third city first? I'm a bit worried that I neglect growth too much when I focus on military for a lot of turns now.
Small cities are great in CIV, because they cost less maintenance. That's not so important for your capital, because your capital has the Palace, which reduces maintenance significantly, so try to let your city grow to happy-cap once you got like 3-5 cities. When you build military, your city can grow, so building military and Growth doesn't contradict each other. Expanding and growing does, but expansion should always be given the highest priority. Question is: Can you expand cheaper with Keshiks than you can with Settlers. If the question is yes, go for Keshiks. You should finish the Library though, because a Library in the capital is mandatory.
_ With that additional fish tile on the coast X2 looks like a potential food monster city candidate. But Seraiel said earlier in this thread that even 3 food resources are too much for a single city. However, in the guide I am reading there are cities mentioned that act as a "Great Person Farm" and that those cities should have as much food and citizens as possible to employ as many specialists as possible in order to produce great persons. Wouldn't X2 be a good candidate for such a city? Or is it still better to aim for 2 cities on the coast? (Not sure however where exactly. Maybe one must be a few tiles east from the coast...)
One city should have as much Food as possible to work as a Great Person (GP) Farm, that's right. If you want to assign X2 for that, it's fine. I usually try to get more cities, and work with multiple smaller GP-farms, so instead of hiring 8 Specialists, which requires you to run Caste System, I go for 4 cities and hire 2 Specialists in them, which lets me stay in Slavery and only requires me to build some Libraries.
The best tactic to produce GPs, is to have many larg(er) cities, and trigger a Golden Age with consuming one GP, then switch to Caste-System + Pacifism to greatly enhance GP-production (the Golden Age (GA) also gives +100% on GP-production, so you can get up to +300% with the NE and +200% in normal cities) , and then hire as many Specialists as possible in all of them, while starving them to the point at which they would lose a population point at the next turn. Ofc you don't want them to shrink, but you want to maximise the bonus you can get from the GA.
Hth.