Welp, TIL. Thank you. :)

While absolutely conceding the synonymous property of the two phrases, I will further confess to never having encountered the francified version, which seems unfair since they had it first.

As a reference source I bristle at Merriam-Webster's citing only four recent examples from current year (2026) and one more from only a year earlier. That's utterly -- nay, actively -- useless to establish provenance or actual etymological information. But that's on par for M-W. Etymonline's result for "petty" was more useful.

A DDG search on '"petit theft" provenance' results was more fruitful, and maybe where your own AFAICT info came from(?):

• A Tallahassee legal firm's blog entry from 2024
• Another (undated) blog source at BustedBaddie.com which cites Florida Statute § 812.014, in which, sure enough, the crime is so named.

I'll chalk-up the difference to mutual provinciality and the Atlantic USAian coast's complicated history with the French. ;-)