That makes no sense; in both cases the pronunciation is not that used in French.

• “et une” is pronounced e yn; listen to the pronunciation of “une” here.
• “j’ai une” is pronounced ʒɛ yn; ʒɛ is pronounced as in “gène” (without “ne”);listen to the pronunciation of “un gène” here.

I see no contradiction between this “en”, or in French “énn” /en/ and Jane pronounced /ʒen/.

This pronunciation where the /y/ is partially or totally dropped (apheresys) is indeed common in spoken French :

J’ai une faim de loup : /ʒenfɛ̃dlu/ (j’ainn’ faim d’loup) or /ʒɛnfɛ̃dlu/