OK, he was a German red deer first. But the Bambi that the world knows and loves—friend to Thumper, wooer of Faline—was actually a white-tailed deer from Baxter State Park in Maine, as this article in the world's best magazine proves definitely.
PS. Among hunters, Walt Disney's Bambi is the most hated movie ever because they blame it for transforming what had formerly been a socially accepted pastime into a perceived bloodsport pursued only by closeted homicides. My own take is: Bambi isn't all that pernicious (man does enter the forest, after all), but anthropomorphizing animals is naive and an expression of humanity's abiding narcissism. Also, most of the hunters I've known are highly moral people who are far less likely to inflict violence on other human beings than the urbanized Major Nidal Hasans and Seung-Hui Chos of the world.