We've found them!
2650 B.C.: The Celts encounter an expedition from the Swedish tribes to the Northeast.
I'm starting to get pretty nervous. England, France, Germany, Sweden, and Russia... adding myself makes six. That's fully half of the major civilizations on the map, and I've run into them long before trans-ocean sea travel is possible. This means I've spawned on some sort of Eurasian super continent, which is tough considering you can be attacked by a lot of different people at a lot of different angles. Being on an island with only one or two other civs is a much better position to be in.
2600 B.C.: Celtic scouts discover the location of the French capital, Paris, and the small outlying city of Lyon. They are found and killed shortly after reporting this discovery.
It looks like my men have a long march ahead of them--it's 9 turns from Dublin to Paris. A lot can happen in that time, and that's assuming I don't have to stop part-way to deal with barbarians.
2525 B.C.: The French chieftain proposes a peace treaty that involves the Celts paying him a large sum of gold. The Celts send the messenger's head back with a single gold coin in each eye socket.
This behavior of Civ V's AI never ceases to annoy me. Even when they're losing, some leaders will propose peace treaties that involve the attacker paying them ransom or tribute. Needless to say, it only made me want to burn their crops all the more.