The OED has s.v. "-ish suffix 2":
A suffix of verbs, representing French -iss-, extended stem of verbs
in -ir, e.g. périr to perish, periss-ant, ils periss-ent. The French
-iss- originated in the Latin -isc- of inceptive verbs, which in Italian, Provençal, and French was extended to form a class of simple
verbs, corresponding to Latin verbs in -īre and -ēre, and including
others which were assimilated to these. At their first adoption, these
verbs ended in English in -is, -ise, -iss(e, which before 1400 changed
to -isshe. In Scottish the original -is, -isse, was retained longer,
and appeared in 16th cent. as -eis(e: pereis, fleureis. Among the
chief examples of this ending are abolish, accomplish, banish,
blandish, blemish, brandish, burnish, cherish, demolish, embellish,
establish, finish, flourish, furbish, furnish, garnish, impoverish,
languish, nourish, perish, polish, punish, ravish, relinquish,
replenish, tarnish, vanish, varnish. In some cases, other French
endings have been levelled under this suffix in Anglo-Norman or
English: such are admonish, astonish, diminish, distinguish, eternish,
famish, lavish, minish, monish, publish, relish, etc., for the history
of which see the individual words.In a few words the French -iss- is
represented in English by -ise, or even -ize: e.g. avertir, -iss-
advertise v., châstir, -iss- chastise v.; amortir, -iss- amortize v.;
réjouir, rejouiss- has given rejoice n.
No mention of Picard.