In a medium saucepan, combine lentils and 4 cups water. Bring to a boil; reduce to a simmer. Cook until lentils are tender but not mushy, 15 to 20 minutes. Drain well.
Meanwhile, in a medium skillet, cook bacon over medium-low heat until crisp, 8 to 10 minutes. Using a slotted spoon, transfer to a paper-towel-lined plate to drain.
Add onion and carrots to rendered fat in skillet. Cook, stirring occasionally, until carrots are tender, 15 to 20 minutes. Add garlic, and cook until fragrant, about 2 minutes.
In a medium bowl, whisk together vinegar, Dijon, and oil; season with salt and pepper. Combine frisee and 1/3 of the dressing in another bowl; toss to coat. Add lentils, onion mixture, and bacon to bowl with remaining dressing; toss to coat. To serve, divide frisee among salad plates; top with lentil salad.