I put "I was at the point of entering when I saw the smoke" and was marked wrong.
Surely, the saying "to be at the point of (doing something)" exists in the English language as well..
I also reported this translation as correct.
edit: and "I was on the point of entry when I saw the smoke"
Point of entering, fine. But "point of entry" indicates a location, usually a door.
Être sur le point de = "to be about to".
To be on or at the point of entering = To be about to enter. Both are valid translations
Should be accepted: "I saw the smoke when I was about to enter. " Reported.