The First Synod of St Patrick (457AD) says

14. A Christian who has committed murder, or committed adultery, or sworn before a druid as pagans do

Which indicates that druids are still active, but probably by that point, on the way out. The 7th century Vitae Brigitae talks about a meeting of St Brigit's foster father (a druid) and the church in the 6th century, which would tie well together with Diarmait Mac Cerbaill (560AD) who was a patron of Druids, but he died in 565 and was probably the last real king with pagan beliefs in Ireland. So you've got perhaps until the mid 6th century.

That's the British Isles - I can't comment for the continent, but considering the spread of Christianity, I'd imagine it would be similar.