I understand it as being a button for jogging the hole punch function on a machine, i.e. refreshing it, possibly resetting it to a reference position, or for performing the task manually, once at a time.
It seems that there is no existing equivalent in French, so I would use the English term followed by a brief explanation.

EN punch = FR perforatrice / fonction de perforation
https://fr.other.wiki/wiki/Hole_punch(bilingual site)
http://www.wikiwords.org/dictionary/term/769940/1481962
https://www.proz.com/kudoz/english-to-french/tech-engineerin...
(many other examples available elsewhere)


Here are a few ideas for "jog" or "jog button" or "jogging button" - if you are looking to add an explanation in French after the term:

ENGLISH

jogging button
[Google books link]
https://books.google.fr/books?id=kgkEDj5TRh8C&pg=PA150&lpg=P...
By jogging, the operator brings the tool to the reference position and sets this position through the control panel as (0,0,0).

https://patents.google.com/patent/JP4909652B2/en
...the jogging button is operated to rotate forward at low speed to the predetermined rotation phase...

https://www.carotron.com/instmanlist/ChoiceSer.PDF
When the JOG button is pressed and released, the reference is immediately clamped to stop the motor but the contactor is held energized for four seconds. Pressing the JOG button again within the four second "delay" period will cause the motor to immediately jog and will reset the four seconds delay.


FRENCH
https://www.festo.com/net/SupportPortal/Files/406387/CDSA-SW...
(pdf download, see Fig. 2.1)
Panneau de commande Jog (pas à pas)

https://www.cpmo.fr/attachment.php?id_attachment=45
(pdf download, see text at bottom of page 4)
"Les presses plieuses équipées du contrôle CADMAN Touch disposent d'un bouton jog sur la pédale pour permettre à l'opérateur de commander manuellement les axes individuels de la machine pour des réglages fins."

impulsion (par pédale électrique)
https://www.soremat.fr/pdf/4291.pdf

https://www.soudeuses-pro.com/soudeuses-eco/soudeuse-automat...
SOUDEUSE AUTOMATIQUE 450T /5mm pour P.P,P.E a impulsion par pédale électro-magnétique.

https://www.expressio.fr/expressions/rafraichir-la-memoire
jog your memory = rafraîchir votre mémoire


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Note added at 2 hrs (2021-05-09 16:24:33 GMT)
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Sorry, my first series of links contained errors:
EN punch = FR perforatrice / fonction de perforation
https://fr.other.wiki/wiki/Hole_punch
https://www.proz.com/kudoz/english-to-french/tech-engineerin...
(many other examples available elsewhere)