Learn English – Pronunciation of Middle English

The list of en- words that can be pronounced /an/ rather than /ɪn/ or /ɛn/ is pretty short. From a quick search of the Carnegie-Mellon Pronouncing Dictionary, these words start with en- and can be pronounced /an/ (some have alternate pronunciations with /ɛn/):

ENCLAVE
ENCLAVES
ENCORE
ENCORES
ENFANT
ENSEMBLE
ENSEMBLES
ENTENDRE
ENTOURAGE
ENTOURAGES
ENTRE
ENTREE
ENTREES
ENTREPRENEUR
ENTREPRENEUR'S
ENTREPRENEURIAL
ENTREPRENEURS
ENTREPRENEURSHIP
ENVOY
ENVOYS

I will note also that Merriam-Webster does also countenance /an/ for envelope. However, few if any other en- words can be pronounced /an/.

Nearly half of these words (not to mention others, like buoy) seem to be related to seafaring or fishing:

block, deck, hoist, leak, plug, pump, smelt, stern, trigger.

And one can imagine that many of the others might have come into the language through sailor's lingo.

Maybe you should narrow down the question to: how closely did Dutch and English sailors interact in the Middle Ages? Maybe fishermen moonlighted as smugglers back then, and got to know their Dutch counterparts fairly well. Or maybe some ships had multinational crews.