I thank you for providing this information in such a polite manner. I hope Im able to do the same as Im mot trying to cause offense. This is an attempt to put together what info I have on the subject, so read on if interested.
If one is quoting its likely originator Shakespeare, itd be hoist with his own petar(d), but if following decades of popular use either hoist or hoisted is generally accepted. A petard is an explosive device rather than an impaling one, so it makes more sense to say one is hoist(ed) (raised up) by or with one rather than on. When I first read or heard the expression not knowing what a petard was, I imagined someone being lifted after being impaled by a sword. Yet, years after learning a petard is neither not an instrument by which you can impale someone and then lift them up like in Medieval fiction, it still comes to mind before the, lets say, antics of Wile E Coyote. Wile E Coyote who has made a career out of being harmed by or with his own designs. I suppose he has at times hoisted himself on his own petard whenever hes straddled an Acme rocket to catch the roadrunner, but that has different meaning.
Although petar(d)has its roots in French, hoise and its past participle hoist (hoised) have there roots in Middle English (Germanic). I dont believe the expressions origin is French rather than another attributable to Shakespeare (Hamlet). Hoisted is now the past participle for hoist and commonly used with this expression. Justice Matterss use here is commonly accepted outside of English literature classes and isolated cocktail gatherings.