It costs a few more miles, but have you tried breaking up the searches to the separate legs i.e. PER-SIN and SIN-CDG?
I'm from Perth and there is often more availability when doing it that way, as there is different inventory when searching PER-CDG vs the separate segments.
I just did a dummy search and 3xJ savers PER-SIN were not too hard to find, but the SIN-CDG segments didn't have any luck (only searched a few random dates).
As mentioned above, finding 3 J awards on the same flight can prove difficult. We've managed 2x suites previously so 2x savers will also increase your chances if splitting the flights is an option (not always possible I know).