The locution fol nestre may be influenced by the meaning of nastre#1 in form.
Langlois (ZfRP, XXXI, 220-25) suggests that natre is a syncopated form of villein nastre, though all of the attestations here predate the earliest attestation of villein nastre. FEW repeats Langlois’ theory, which is also mentioned in the OED’s etymology of nasty, which, while similar in form, does not seem to be semantically linked. All other dictionaries include the expression fol nastre in their entries for nastre and not in nestre, except for the English dictionaries where the expression is found under natural.
As both nasquir and nestre have identical conjugations in the preterite, it has seemed best to include the forms under the more fertile nestre, unless their form shows they clearly derive from nasquir.