The Roman Republic was an influential state to the Mediterranean, but their northern boundary never proceeded farther than what they called Gallia Narbonensis and Gallia Cisalpina.
What sort of situation would be required for the Romans to conquer land north of the Alps--perhaps even all of Gaul?--and if they did, how would it change the history of Europe?
Would those areas speak Latin, much like Italia, Hispania, and Africa do today?