Btw, Stuttgart is only 3h by train from Paris.
Tickets are not cheap but if you have travel insurance this may be an option:
Fri 17 Feb,
12:31 London St-Pancras
15:59 Paris Gare du Nord
2h 28m
ES 9024
1h 56m to change stations
17:55 Paris Gare de l’Est
21:04 Stuttgart Hbf
3h 9m
TGV INOUI 9579