Heat oil in large saucepan over medium heat until shimmering.
Add onion, carrot, celery, and salt; cook until vegetables are tender, about 5 minutes.
Add broth and lentils and bring to simmer.
Reduce heat to medium-low; cover; and cook, stirring occasionally, until lentils are tender but still hold their shape, about 30 minutes.
(Add hot water, ¼ cup at a time, if saucepan becomes dry before lentils are cooked through.)
Gently fold in spinach and mustard.
Let sit off heat for 5 minutes.
Transfer to serving bowl and dollop with crème fraîche.
Serve.
