Civics
I am presuming "I am going for cultural victory" is the case, and certainly agree with Kate on the appropriateness of your civics in that you can leverage your Specialist Artists and settled Great People more effectively while getting a massive

surge from Free Speech.
Where you are;
Where you might want to be;
Unfortunately 5 turns of Anarchy to get there!
Food
I would suggest that you have a disproportionately low number of Farms that that acted to restrain the population levels of your cities, as you've not 'chain irrigated' into areas with low natural food production.
Chartres is an example where it's so food-poor that it can't even work the Gold Mine, while stealing the Cows from near-by Marseilles will only put that city into starvation;
Now clearly a Lighthouse would provide a heap of 2

tiles, but it's really the lack of food from land tiles that could do with review.
Another one? Kate noted Orleans;
It is making a handy contribution to your empire with those developed Cottages > Towns, but it will be unable to work any of those Mines or the Quarry. Biology will give your Wheat Farm another

, but certainly not the wholesale elevation in food production required to support the Mines.
Avignon has a different problem - Jungle is making the city unhealthy, but you have idle Workers who could be clearing the Jungle away and not only fix the unhealthiness, but create far more useable tiles;
From Here
If you're still going to pursue a Cultural victory, then you're almost certainly going to have to go after the late game Cultural Wonders and could boost this by going with some of the

-providing Corporations such as Civilized Jewellers - as such, press on with your technological leadership down that 'Mass Media' path. Unlike Kate, I'd keep up the science push until you're comfortable with the technologies that you have or can trade for before turning up the Culture slider. Moving out of Hereditary Rule
may require you to put some

to

just to deal with unhappiness.
If you want a Christian Cathedral to be built in Paris, then you'll want another city (maybe near the Spices in the south east) and for that city to have Christianity spread to it so it can build your ninth Christian Temple. Unfortunately you're so close to Scientific Method that trying to pick up and spread new religions without Monasteries (i.e. through Organised Religion) may be more effort than it's worth.
I would say that you are completely safe from any attack at this point. Germany and Portugal are both Friendly and neither 'has enough on their hands', while no rival tribe has Astronomy. As Kate suggests, you might want to be mindful of an invasion at some later point however, and going after Rifling + Assembly Line or even Industrialism once you have acquired Mass Media could be worth considering as the AI improves its capacity for invasion.
A final note - Cultural wins are a lot about timing so that you minimise the waste of

in cities that have already gone legendary, so think carefully about where you'll be putting those last World Wonders and when and where to 'build Culture'.
Other victories
Unfortunately the Apostolic Palace Diplomatic victory is going to be tough – you can’t spread Christianity in Russia or Spain as both have adopted Theocracy, and Isabella will be reluctant (to say the least!) to move out of her favourite civic. The alternative then is to invade Spain and hope/encourage Catherine to flip out of Theocracy if not invade Russia also. You might be able to pull off a stunt involving capturing a foreign city, spreading Christianity in it, and then gifting it back to the original owner.
I think you would probably have a fair shot at a UN Diplomatic win – you could well be up against the very unpopular Catherine, which might be sufficient to get you a long way there. A flip into Free Religion will give you ‘favourite civic’ bonuses with Willem and Elizabeth, but you’ll therefore lose the ‘brothers and sisters of the faith’ bonus with Frederick and Joao. Look for ways to boost your own voting power.
With your technological lead and decent sized empire there’s little reason to suspect that you can’t pull off a spaceship win, but it’s unfortunate that you’ve spent so much effort spawning Great Artists to then redirect your efforts away from a Cultural win.
Both Conquest and Domination I’m sure are do-able. With your technology lead and some severe backstabbing you should be able to take out Germany and Portugal with a couple of SoDs on Industrial Age weaponry, and take on the other continent with more modern warfare.
Hope some of this helps!