This unique adverbial use of ordenaire does not reflect the senses of the adjective, but functions (in error perhaps) as a synonym for ordenément or ordenalment.
adv.
1in orderly fashion:
(
c.1215; MS: 1330-40
)
Puis vit issir mout bele gent, Deus e deus ordeinerement (var. (P: s.xvin) moult ordenément)640
[ordenairement] (c.1215)