In a large heavy skillet, melt the butter over medium-high heat. Add the garlic, shallots, basil leaves, and pepper flakes, partially cover, and cook over low heat for 1 to 2 minutes. Uncover, stir in the plums, peaches, and tomatoes, and cook for 2 to 3 minutes until they start to soften. Add the sugar and cook until melted. Stir in the vinegar and cook on low heat until the fruits are completely soft, stirring occasionally. Transfer the mixture to a food processor or the jar of an electric blender and puree until smooth. Season, to taste, with salt and pepper. Pour into a bowl and set aside.
Lightly brush the salmon with olive oil. Season it with salt and pepper. Heat the remaining oil in a large skillet over medium-high heat. Add the salmon and pan roast it until lightly browned, about 3 to 4 minutes. Turn and cook the second side for the same amount of time for medium-rare, or 5 minutes for medium. Remove and serve each fillet with a generous spoonful of fruit salsa drizzled on top. Pass the remaining salsa at the table.