From what I have read, reading the histories of Norwegian Spitfire squadrons (Under RAF) as well as "The Big Show" by french pilot Clostermann, it seems they got the heads up very, very, close to the event. Like the 4th or 5th of June. They off course knew the invasion was imminent, they trained for it extensively, but that it was june 6 and Normandy seemed to be known very late (although I suspect many had put their money on it before the announcement). If I remember correctly, Clostermann knew about it a few days before, due to some assignment, and was not allowed to fly until the the invasion was underway (So he would not get shot down and captured).