"J'étais sur le point d'entrer quand j'ai vu la fumée."

Translation: I was about to enter when I saw the smoke.

[AdrianDan22]

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..

[b_adger]

I also reported this translation as correct.
edit: and "I was on the point of entry when I saw the smoke"

[--Roody--]

Point of entering, fine. But "point of entry" indicates a location, usually a door.

[GScottOliver]

Être sur le point de = "to be about to".

[oscarhugo52]

To be on or at the point of entering = To be about to enter. Both are valid translations

[LesAussi]

Should be accepted: "I saw the smoke when I was about to enter. " Reported.