I took another look at the New Orleans Archdiocese records, hunting for name variations. Name spellings are notoriously inaccurate in the early records. Also, "Robert" isn't super-common during that period, so I browsed for that name also.
I found one possibility to consider, a Robert GUILLAIN or GUILLEIM, from Cambrai, master shoemaker, about 34 yrs old, buried 20 Jul 1727. This Robert's inferred birth would be about 1693, so it's a few years off, and the birth location doesn't fit. But birth info is not reliable on burial records, especially if there were no family members to provide the information. The main reason he caught my eye is that your Robert's father was also a shoemaker per his profile. Anyway, something to consider.
You can see this volume online in PDF form here: Volume 1 (1718-1750), page 125. It cites the archives in Paris, so perhaps if it's available online you could access it there to review the handwritten record, noting that it wouldn't be the original, but a copy of an extract.
If you decide to use this in the profile, I can provide a citation for you. Just let me know. Hope this helps!