Canon derailment, possibly Heathen idea: Voldemort either died at 1981 or Pettigrew was caught and arrested so Voldemort stays in Albania, stewing in impotent rage.
At the latest during the third year, Harry gets into the care of Sirius and Remus. Since he doesn't have Dementors and constant danger hanging over him, Harry enjoys the year, besides Quidditch taking interest in Dueling, since he is good at Defense, Charms and Transfiguration. Sirius and Remus take Harry on holiday to France, to see the sights, maybe to see a duelling tournament.