Apparently it's an unincorporated place, as it doesn't appear on maps or the US Geographical Survey (USGS). It is, however, mentioned on a death certificate.

Does the death certificate say what Parish?
In Lafayette Parish or another Parish?

No, it does not. I posted this message to the Lafayette Parish board because I had found a few mentions of such a place on line.

There was a post office called Paris in St. Landry Parish too, but it closed in 1880, so I doubt it would have been on a death certificate from the 1960s.

Have you looked to see if this person is listed on social security death index?
That would give you the Parish in 1960.

This person died young and is not, therefore, listed in the SSDI. Perhaps someone who lives in Lafayette Parish would know where Paris is located.

What year was this death certificate?
Also, this is kind of far-fetched, but here goes: Is it possible that the person filling out the death certificate just took a short cut and wanted to say that the person died in the parish (paris) as opposed to inside the city limits? I've heard older people put it that way.

http://louisiana.hometownlocator.com/la/st.-martin/saint-mar... Results: Alternate Unofficial Names: Le Poste Des Atakapas, *Petit Paris*, Saint Martinsville.
(This map pins Paris as being in St. Martinville.) My best guess would be that it's one of those old time towns that got swallowed up by bigger cities.

You might ask on the St. Martin Parish board and also contact the area genealogy / historical society.

This death of a young person is in the 1960's so I'm sure they wold not still refer to the location Le Poste Des Atakapas "Petit Paris". My guess this person died in this Parish, "paris" not spelled out, which I have seen on many records.
They also say its in Lafayette or possibLe St Landry But the Parish is not listed on the death cert. for 1960. ODD! MHO

The location indicated on that map has no particular significance. Don't know why they pinned it.