Preheat the oven to 350°. Butter and flour a 10-inch round cake pan. In a large saucepan, bring the maple syrup to a boil over high heat, then simmer over low heat until very thick and reduced to 3/4 cup, about 20 minutes. Pour the thickened syrup into the cake pan. Arrange the apples in the pan in 2 concentric circles, overlapping them slightly.
In a bowl, whisk the flour, baking powder, baking soda and salt. In a glass measuring cup, whisk the eggs with the buttermilk and vanilla. In the bowl of a standing electric mixer fitted with the paddle, beat the butter and sugar at medium speed until fluffy, about 3 minutes. Beat in the dry and wet ingredients in 3 alternating batches until the batter is smooth; scrape down the side of the bowl.
Scrape the batter over the apples and spread it in an even layer. Bake the cake for 1 1/2 hours, until golden on top and a toothpick inserted in the center comes out clean. Let the cake cool on a rack for 45 minutes.
Place a plate on top of the cake and invert the cake onto the plate; tap lightly to release the cake. Remove the pan. Let the cake cool slightly, then cut into wedges and serve with crème fraîche.