It's too soon to say, but Tallinn, Estonia (pop. 425,000) is now by far the largest city to offer fare-freefree public transit — not just in Europe but anywhere in the world as near as I can tell. Most other free-transit communities are either university-dominated small cities (like Chapel Hill, North Carolina and Hasselt, Belgium) or rural networks where ridership is so low that fares don't pay for the costs of fare collection technology, let alone contribute toward operating cost.
Tallinn — along with Hasselt and the small city of Aubagne, France — are also forming the Free Public Transport European Network, to spread the idea and disseminate experience about it.
As the city's webpage explains, Tallinn citizens must still buy a farecard, which will allow them to ride free. This allows the transit network to continue to collect fares from tourists and people living in other cities.
This raises the interesting possibility that any city, inside a bigger metro area with a regional transit system, could elect to subsidize transit fares for its own residents, by simply buying fares in bulk and giving them away to its own residents — just as some universities and employers already do for their own students or staff. Indeed, smart farecards make it possible for anyone to subsidize fares without much complexity, opening up a huge range of subsidy possibilities for any entity that sees an advantage in doing so. Yet another reason that city governments are not as helpless about transit as they often think, even if they don't control their transit system.