I won my first game on Prince as France. Culture victory, obviously. Started off Paris in a place with a huge amount of food (flood plains) and some gold, but little production aside from the gold. I managed to nab the pantheon that gives you culture and faith from gold, and settled a new city on the coast to secure some more gold deposits. My neighbors were the Netherlands and Venice, which I was in good standing with the entire game. A bit further to the north were the Indonesians, who I also got along with perfectly well. So I just developed a huge amount of culture, waiting before researching some early techs so I could rush ahead and nab wonders. My workers quickly improved all the area around my cities, so I sent them off to build roads in other civs for shits and giggles.
Some other civ founded the World Congress, revealing the civs I didn't bother to go looking for to be Sweden, China, Portugal, Spain, Zulu and India. Despite putting in basically no effort towards the World Congress, I could make a proposal, so I suggested and managed to pass Arts Funding. I traded my gold with all of the other civs for money while continuing to be friendly to everybody. Didn't fight a single war the entire game. I just kept doing what I was doing, more or less constantly building wonders in Paris while my second city gave me some support and storage slots for great works.
Going into Freedom, I was outculturing everybody and somehow also outteching everybody. The only civ which I wasn't quickly gaining influence over was India, who appeared to also be going for a culture victory based on his culture bombs against me. Sadly, he was obnoxiously far away so culture bombs took about twenty turns. So I focused on increasing my cultural output in any way I could instead (theming bonuses, nabbing artifacts from areas which weren't *quite* in other nations' borders, more wonders). This eventually worked! First win on Prince!
E:
Also, Paris had 44 population at the end of the game, which seems slightly ridiculous.