We don't yet have a consistent way of adding new postal codes. We would like to integrate the postal codes with the main database. For some countries we have started to add them as alternate names with the pseudo language code 'post'. France is more or less complete.
You can add postal codes as alternate names to a place name, though they will not immediately appear in the postal code listing.
You can also send me a file and I insert the codes directly into the database.
I attempted adding a Canadian postal code ('A1V 0A9') as an alternate name for Gander (populated place in NL), and found that whenever I inserted 'post' as the language code, an error was returned:
"invalid postal code format for country CA, the format is A9A 9A9*"
I believe the format of my input postal code matches the format in the error message, though I tried with the * at the end also just in case, and got the same error message.