Heat the olive oil in a large pot over medium heat. Add the onion and cook until it softens, about 4 minutes.
Stir in the garlic and cook for 1 minute more. Add the celery root and carrots. Cook for 5 minutes, stirring now and then.
Pour in the white wine. Let it simmer until reduced by half, about 3 minutes.
Add the fish broth. Bring the mixture to a gentle boil, then lower the heat and simmer until the vegetables are tender, 15 to 18 minutes.
Season the red snapper pieces with salt and pepper. Add them to the pot and simmer until the fish turns opaque and flakes easily, 5 to 6 minutes.
Remove the pot from the heat. Stir in the fresh tarragon. Taste and adjust salt and pepper as needed.