Bonjour Julie,
If ‘fait’ in placed before an infinitive verb, ‘fait’ is invariable and therefore doesn’t agree with its subject, even if it is placed ahead. It is a valid rule if you use ‘avoir’ as auxiliary and with ‘être’ as auxiliary in a pronominal phrase in certain circumstances as the link below will explain.
‘Avoir’ as auxiliary:
C’est la tarte que j’ai fait cuire hier = it is the tart I cooked yesterday
Je les ai fait attendre = I had them wait
‘Être’ as auxiliary in a pronominal phrase: see link here
I hope this is helpful.
Bonne journée!