Your sentence is also correct but has a slightly different meaning.
Stephane was going to miss his meeting if he didn't hurry. -- Stephane allait rater son rendez-vous s'il ne se dépêchait pas
Stephane would missed his meeting if he didn't hurry. -- Stephane raterait son rendez-vous s'il ne se dépechait pas.
-- Chris (not a native speaker).
Sorry, I made a typo in the second example:
Stephane would miss his meeting, ....
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