I have operated both types of engine.
If the CFM autostart fails then it can perform up to 3 start attempts each with a dry crank in-between. The FADEC will perform this automatically reducing the fuel schedule in stages but using both ignitors.
The IAE is different as it would NOT perform another autostart after a start failure the ECAM will just display ENGINE MASTER (AFFECTED 1(2)) .......... OFF after it has performed an auto crank.
I hope that helps.