A factory reset on the Fairphone 2 doesn’t install Apps. It removes all user-related data and Apps.
The Orange App was included in an update …
https://support.fairphone.com/hc/en-us/articles/115004090223
Not quite. Fairphone are currently rolling out Android 7, you should be getting it soon. Check the Updater App regularly … and backup or sync your important data, contacts, etc. to somewhere safe beforehand.
In general, Apps can cause bad effects.
A notorious example for wreaking havoc on the Fairphone 2 is the official Facebook App.
Whether the Orange App could cause your problems can only be determined by getting rid of it one way or another … perhaps it will be gone after the Android 7 upgrade (I don’t know)?
Or you could try a different OS temporarily … I don’t know whether the Orange App is also part of Fairphone Open OS … but I certainly think that it isn’t included in LineageOS.
Or you could contactsupport.