During WW1 Picot issued patriotic cards including illustrations of children. These give his full name. (A name was required by the Visé regulations though I think it was the printer's name the must be given). The plane shown in card no. 60 is the "Taube" (dove), an early German fighter only used in combat early in the war, which from below had a very bird-like planform. It was well-enough known to be the subject of a Dubonnet advertising card without actually appearing in the picture. See also Boige and en.wikipedia.org/wiki/Etrich_Taube.
In Bottin 1925 he shows the marques J.P., GIL and JOAN. Bottin just shows these as letters rather than as images. In Bottin 1930 he shows no marques and the entry is as a seller of "best cards of all editions". Also in Bottin 1930 there is an entry for Jaudel (J Petitjean) which now claims the marque J.P. amongst others, also just in printed form. So it is not clear whether JP Paris 142 or the En Promenade cards shown here are Picot or Jaudel cards.
I haven't seen the GIL or JOAN marques. There is a later use of gil/Gil as a marque by Editions Gil, Annecy, and there is also an illustrator who signs cards Gil.
There have been earlier and later JP logos as shown below, both on cartoon cards, which may or may not be related to Picot. They are strangely similar. The Humbert affair featured on the undivided example was very newsworthy at the time and features on cards from several publishers.