I'm not convinced that the dominant occurs in a prominent enough role in "Douce dame jolie" to count as a reciting tone.

Just so we're singing from the same hymnsheet

On the other hand, the progression is quite a bit like the examples in these (scroll to the end):

Seyir of the huseyni mode
Seyir of the neva mode

which give the expected melodic path of the nearest Turkish equivalents to mode I - note how they zoom up to the octave in the second half, and then fall through the whole range, in the same way as Machaut's song. Turkish/Arabic theory was less bound by a small repertoire of melodies than its Christian parallel (which started out with the intention only of cataloguing psalm tones). That is, there was a modal theory which could have described "Douce dame" realistically, but it didn't get to the right place at the right time.