The story
- Middle French · derived fromaller“go”
- Middle English · inherited frombeen goyng to
- English todaybe going to
From Middle English been goyng to, first attested in 1483—some earlier attestations have been claimed, though these are disputed—and grammaticalized over the course of the Early Modern period. Possibly influenced by the comparable use of Middle French aller (“go”), which arose somewhat earlier and is preserved in modern French.
Etymology from Wiktionary, CC BY-SA 4.0.