Why « au mois de X » but « en X »?

Question

All months of the year are masculine, as is the word « mois ». Why don’t they all use the same preposition?

✅ Je suis née en septembre.
✅ Je suis née au mois de septembre.
❌ Je suis née au septembre (??)

Answer 1

◊ The name of the month (septembre) is used without a definite article¹, so we use en :

• Je suis née en septembre.

and it is the usage to express it that way. As @jlliagre writes in their answer "You need to conform to usage", that means having en followed by le is not done, consider it as a rule.

◊ Usage also says that we do not have the masculine definite article le (and les, du or des²) after en. If you want to use the definite article le (les, du or des) then you must use a different preposition.

◊ You cannot use mois without the definite article, so, to conform to usage we have to use a different preposition that has the same meaning and that allows the presence of the masculine definite article, that is why we say :

• Je suis né au mois de septembre.

au standing for à le³.

◊ Note that the singular feminine definite article is allowed after en :

• Il y a péril en la demeure.

• Je crois en la justice⁴.
  but

• Je crois aux fantômes.

◊ Online resources:
How do you use the French preposition 'en'? (Collins grammar)
English translation of 'à' (Collins dictionary)
English translation of 'en' (Collins dictionary)
En (Lawless French)
À (Lawless French)

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_{¹ We could consider the name of a month is some sort of proper name and we don't normally have a definite article in front of proper names.
² du → de le ; des → de les.
³ À meaning "in" in English. But à can have several other meanings. En can also have other meanings than the English "in".
⁴ You can also say Je crois à la justice, there's a nuance in meaning.}

Answer 2

Prepositions can't be used arbitrarily. You need to conform to the usage. En is the only one used when directly preceding a month name.

Je suis né en juin, (mais fin juin, au mois de juin).
Je suis né un mardi.
Je suis né en 1923.
Je suis né au XX^e siècle.
Je suis né en été, pas au printemps .
Je suis né un samedi.
Je suis né le samedi 23 juin 1923.
Je suis né le matin du samedi 23 juin 1923.

It's similar with locations:
Je suis né à Marseille.
Je suis né dans les Bouches-du-Rhône, pas en Corse.

_{Note: dates and locations above are fictitious. ;-)}