Latin pipire, to chirp, lies behind Late Latin pipio, a young bird. The name entered English through French.
Pijun is one of the French variants, not a stage after the alternative pygoun. Pipion- is the stem of pipio, not another chronological step. Middle English is omitted as a separate card.
Sources
- Merriam-Webster: pigeon
Noun (1) Word History gives pipire, pipio/pipion-, the French variants and the Middle English borrowing.
- Anglo-Norman Dictionary · pigon
Meanings of the older forms on the word path.
- Online Etymology Dictionary · pigeon
Meanings of the older forms on the word path.