Yes “finissait” is the right answer here, but the verb “terminer” is more appropriate here.
Thank you for your comment! Yes, one can use 'terminer' (a more literary option) as well as 'finir' in this instance. As such, a hint is given for this question: Conjugate "finir" (to finish) in L'Imparfait
Please see link here for a discussion on a similar topic: choice-of-infinitive-for-we-have-just-finished
I hope this is helpful.
Bonne journée !
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