Here's some comments I have about that game:
Too few workers. You only have 5 workers for 8 cities. You need more, especially with all that jungle you need to clear. Since it is already 760 A.D., I suspect you had less than 5 workers for much of the early game (B.C. years). You are industrious, so you should have a MINIMUM of 1 worker/city, more if you hadn't been industrious. And get those workers built ASAP. After your expansion phase, each city should have built a worker. For me, new cities have a build order of warrior, worker, warrior, (depending on it's shield output) then it can start on other things. Sure, now nearly all your citizens are working improved terrain, but I suspect that many of them spent most of the game working on unimproved terrain.
City placement. You bypassed some bonus resources. The game north of Paris is unused. I would have moved Tours one tile southeast so it could claim the game on forest. Yes, you would then give up the whale, but the game is more valuable, IMHO. You would also pick up 2 more plain tiles and have less overlap with Rheims. You have many unused tiles between Avignon and Lyons. I would have done 1 of 2 things. #1. I would have moved Avignon one tile southeast to pick up the fish and getting more plains/grassland/jungle (which after being chopped down would be plains/grassland) instead of working all that desert. Or #2. Move Avignon more to the north and fit a city in between Avignon and Lyons and the new city would claim the fish. And then there is the fish southeast of Lyons that's not used which complicates the city placement pattern.
Now that you are a republic (or any government besides despotism), you can irrigate some of that grassland by Lyons so that you'll have excess food to be able to work some of those mountains and hills. Easier to do if you had more workers.
30% science? You have the Great Library. Go with 0% until that expires. If you did not have the Great Library, you'd be better off going with 0-10% science instead of 30% and just buying techs. Either go with no science or max science (over 50%, which you can't afford to do).
Build marketplaces. That will greatly help your income. Paris wouldn't have needed a courthouse until much later in the game usually (after hospitals or when you get tons of cities). I don't build a courthouse in the capital unless I actually see it losing some shields/commerce. Instead of the courthouse, it could have built many other things (even workers/settlers) instead.
Buy contacts. The great library will only give you techs that other civs you KNOW have the tech. Plus knowing more civs will make buying or researching techs ALOT cheaper (especially if you are behind in techs). Plus, you'll have more options in trading and selling. Buy communications of the Japanese, Chinese, and Indians from England by giving her Monarchy, world map and some gold. Then contact India and give him a tech for his world map. I always buy all the contacts I can before buying any techs. I see you were giving away your wine (probably for techs), but you had the Great Library so you shouldn't be buying techs except in some rare situations. If you can trade with Germany to get one of his luxuries that would really help you out. If you could get 1 more luxury, so that you can turn down the lux. rate a notch and go with 0% science, you'll make +42 gold/turn instead of +4.
Chartes is working a coast tile (with no harbor) when there is mined grassland available. Lyons has a bonus grassland that is being ignored, so it is working regular mined grassland. Mine that bonus grassland. I hope Orleans wasn't working those irrigated desert tiles for too long when it had an irrigated plains tile available.
You did an awesome job at getting your cities built early. I know Lyons you got because of a settler from a hut (3700 BC), did you get any other settlers from huts? You had 6 cities by 2590 BC. (29 turns).
Whatever you did after the expansion phase is where you fell behind. Not enough workers being one of them. I see some undefended cities. Were those cities undefended while you were in despotism? If they were then these cities didn't have military police which would cause more unhappiness. Having the military police would allow you to require less luxury tax. Just build warriors for military police when you are on an island all to yourself. They are cheaper to build (you want 2 military police and 2 warriors cost the same shields as 1 spearman). With access to only 1 luxury, you may have been better off in Monarchy if you had military police in all your cities (you can have up to 3 military police in monarchy, which would equal 3 content citizens). On warlord level (3 citizens born content) and having 3 military police, and 1 luxury, you would be able to get your cities up to size 7 or 8 without having any unhappy people. This would help trigger WLTK days.