To prepare cake, lightly spoon the flour into a dry measuring cup, and level with a knife.
Sift together flour and 3/4 cup sugar. Beat egg whites with a mixer at high speed until foamy. Add cream of tartar and salt; beat until soft peaks form. Add 3/4 cup sugar, 2 tablespoons at a time, beating until stiff peaks form. Fold in vanilla. Sift flour mixture over egg white mixture, 3 tablespoons at a time; fold in.
Spoon batter into an ungreased 10-inch tube pan, spreading evenly. Break air pockets by cutting through batter with a knife. Bake at 325° for 50 minutes or until cake springs back when lightly touched. Invert pan, and cool completely. Loosen cake from sides of pan using a narrow metal spatula. Invert the cake onto plate. Cut cake into 12 slices.
To prepare compote, combine water, 1/4 cup sugar, and vanilla bean in a medium saucepan. Bring to a boil over medium heat, stirring until the sugar dissolves. Cover, reduce heat, and simmer 15 minutes. Add dried fruits; cover and simmer 25 minutes or until fruit is tender, stirring once. Remove from heat. Remove vanilla bean. Let bean stand 5 minutes. Scrape seeds from vanilla bean; stir seeds into the fruit mixture. Discard bean. Cool to room temperature. Spoon compote over cake slices, and top with crème fraîche.