The French are indeed threatening your cities, but that is not your biggest problem right now. Here is how I would rank your troubles:
1. Your economy is second to last in the world. (F11 screen)
2. You are half an age behind in tech. (The French have industrial age graphics)
3. 3 civs are allied against you. (F4 screen with military alliance checked)
4. Obsolete unit support is eating 40% of your uncorrupted income. (F1 screen)
There are a couple ways you could fix this.
The Builder Way
Pay 7 gold per turn for peace with France (they will talk next turn).
Turn off science spending, it is cheaper to buy techs now. Eventually you will find a tech that some AIs are missing, buy it and then barter it for other techs to get a 2-for-1 deal.
Be sure to pay gold per turn for techs. Your opponents lose their money if they backstab you. And you can start using and trading the tech much earlier than if you saved up the gold/beakers yourself.
Move 13 military units into Seoul. Then
abandon Medina. This is called a
Free Palace Jump, and it will allow many more of your cities to be productive. Unfortunately you have to rebuild the Forbidden Palace, but it will pay off in the long run.
Disband your 15 most obsolete military units, and replace them with 15 workers.
Build marketplaces (and later banks) in every uncorrupt city.
The Diplomacy/Backstab Way
One of your biggest reasons your economy sucks is the Russians have cities in "your" core around the capital. You need to take them over. As an added bonus, the Russians have the Great Library.
Some sneaky diplomacy is needed, since you are so far behind.
We give 6 gold per turn, Ottomans give 100 gold.
Use that gold to buy embassies with Russians and Ottomans (Shift-E).
We give Incense and 1 gold per turn, Russians give alliance vs France.
We give 17 gold per turn, Ottomans give alliance vs France.
Now France will get a major beatdown from both sides. Hopefully that will keep the pressure off you, since you are locked into the alliances for 20 turns. (Cancelling them earlier will destroy your ability to do gold per turn deals.)
Now build 10 more Ansar warriors (20 total). Sign a right of passage with russia and park all 20 Ansars outside of Moscow. Cancel every deal with Russia, using the "Active" link on the bottom of the negotiating table. Declare war and capture the Great Library, hold it for 1 turn, then start upgrading.
This will destroy your ability to use ROPs, but leave your gold per turn reputation intact.
Good luck!
