War is what you need. The most compelling reason for war is not that a space or UN victory is too hard with a 6CC, but that 2 of the 6 cities are under too much culture pressure. Chances are, youre not going to beat a DG AI in culture, so those 2 cities may eventually flip. When those two cities flip, its game over, everything else that you do will be for naught.
I think the target of war should be China, not France. The reason: China is the biggest and most powerful AI, and it's about to becomes even more powerful with a GA due in 2 turns (investigate Beijing will show you why). If you dont stop it now, it may run away with the game. France is weak. They are not a threat to you. The productive cities of France are far away, which means they are not going to be productive for you. The close French cities are tundra cities. Basically, by attacking France first, youre not going to be in a stronger position to take on China later. Not to mention China is one that has the much needed iron, and is putting the most culture pressure on you.
You do have a chance against China in the next few turns. 3 of Chinas 4 best cities are currently building wonders (see the F7 screen). Youre about to research Republic, which 2 of Chinas neighbors do not have. You could use Republic to sign a pair of very valuable alliances. Naking, the iron cities, is guarded by only 4 reg spears,
I really wish you had posted the save about 20 turns ago. All of the infrastructure that was built was basically useless. The best time to attack China was about 5 turns ago, which you could have made if all the shield that was spent on infrastructure was spent on troops instead. As it is, it will take roughly 5-6 turns to get an offensive stack ready, and China will be 3 turns into its GA by then. The war will be much tougher than it could have been.
The stack of units that I recommend to start the war with is about 8 archers, 2 spears, 8 cats, and 2-4 horses. That stack is probably enough to take Naking in the first few turns of the war, and later Shanghai. Beijing will probably require at least 12 catapults and more horses. Because of the 2 alliances that I think you should sign, the war will last 20 turns, so plan accordingly. There should be no rush to capture cities at the cost of units. Play a slow and steady game. Kill enemy units first, then advance. Conserve your forces. The goal is to capture Nanking, Shanghai (the gem city) and Beijing in 20 turns, so there is plenty of time.
Nanking, Shanghai and Beijing will be the most productive Chinese cities for you. The other cities are either too small to distant. If you could get to those other cities, then thats great, but dont use resources that could be spent on the three primary targets on the other cities. Let youre allies take those other cities, you shouldnt have a hard time taking them later should you feel the need. However, if youre close to kick the Chinese off of the main continent by the wars end, then go for it. It will lessen the chance of culture flips by a lot.
After taking Beijing, you can probably stop troop production and start building aqueducts and marketplace in the core. The none-capital cities will be much easier to take than Beijing. Those left over troops should be able to take care of everything. After the Chinese war, should you have too much troop left over for a Republic, consider turning on the French immediately to use up some of them
[edit] almost forgot, it is a Demi-god game
