Preheat a grill or grill pan to medium. In a large saucepan, mash together the strawberries, lemon juice and vinegar and cook over high heat until softened, 2 to 4 minutes.
Spread 2 tablespoons condensed milk on the cut sides of each baguette slice; let soak in 1 to 2 minutes. Grill the bread crust side down until warm, about 2 minutes; turn and grill until golden, 3 to 5 minutes.
Top the grilled bread with the strawberries and let stand for a few minutes before serving.