The programs that I listed are taught entirely in English for the core courses, with mandatory intensive French classes the 1st year and “politics-related French classes” your 2nd year. Obviously a good command of French is required (B1=AP, “independent” - Other levels: B2= advanced - C1= Expert. C2 is Expert/professional, which only academics and translators can hope to achieve.)
If Edinburgh is too expensive, what about Aberdeen?
Either of these 2 should be within reach academically
https://www.abdn.ac.uk/study/undergraduate/degree-programmes/635/LRF1/french-and-international-relations/
https://www.abdn.ac.uk/study/undergraduate/degree-programmes/647/RL12/french-and-politics-5-years/
The degrees are pretty flexible. Automatic £2,000 scholarship, additional £2,000 if you had a 3.8 wGPA (on transcript).
Bath and Bristol are cool cities for students, too, better than Aberdeen, but the degrees are less flexible.