Set a medium bowl in a large bowl filled with ice. In a medium saucepan, combine the lemongrass, chiles, lime zest and sugar with 1 cup of water and bring to boil, stirring until the sugar is dissolved. Simmer until slightly thickened, about 8 minutes. Transfer to the ice water bath and let chill for 15 minutes.
In a large bowl, toss the strawberries with the melon and mint. Strain the cooled lemongrass syrup over the fruit and toss gently. Refrigerate just until slightly chilled.
In a bowl, stir the ginger into the crčme fraîche. Spoon the fruit salad into bowls, top with a dollop of the ginger cream and serve.