Cut the peel and white pith from the oranges. Cut between the membranes to release the segments.
Whisk the vinegar, creme fraiche, and sugar in a heavy small saucepan over medium-high heat until it thickens and resembles a sauce, about 8 minutes.
Arrange the orange segments and strawberries decoratively on plates. Drizzle the warm balsamic sauce over the fruit and serve. Alternately, the balsamic sauce can be served at room temperature and spooned atop the fruit. This is great served with frozen yogurt or ice cream.