On time refers to an event taking place at the exact time it was supposed to take place: the meeting started on time. Expect Swiss trains to run more or less on time.
In time refers to something happening before a crucial deadline/event:
- We finished the proposal in time for the meeting. (Nous avons terminé à temps…)
- The police arrived just in time to see the robbers espace. (La police est arrivée le temps de voir…)
- We arrived at the airport in time to catch the last flight. (Nous sommes arrivés à temps…)
In due time, in due course refers to something being completed in an appropriate amount of time. The committee will study your proposal and provide a response in due time/in due course.
In French, with variations in brackets :
- Je suis arrivé à l’heure→ on time [right on time, exactly on time]
- Je suis arrivée (juste) à temps→ just in time [in the nick of time, just in time]
- Je répondrai en temps voulu → I’ll reply in due time [in due course, when the time comes].