Wildcards Duckworth and Kokkinakis were not expected to trouble their more experienced French opponents in the round of 32, but the Australian duo pulled off straight-sets victories on home soil.
Duckworth had never beaten a player ranked inside the top 30 in the ATP rankings, but the 22-year-old enjoyed his finest hour by winning 6-2 6-2 against the sixth seed in just 69 minutes.
Simon, ranked 21st in the world, was broken five times and managed just one break of his own as he started 2015 with a whimper.
He was immediately up against it when Duckworth won the first four games of the match in ruthless fashion and never looked back, taking his third set point and carrying that momentum into the second set.
Simon was broken immediately in the second and trailed 4-1 when Duckworth claimed another break, with both players failing to hold in the next two games to leave the underdog serving for the match.
Duckworth, ranked 125th in the world, kept his nerve to serve out the match to love to reap the rewards for putting in the hard yards ahead of the new season.
"I had a really good pre-season," Duckworth told the official ATP website.
"[I] trained really hard up here. I was used to the conditions…It was just a matter of transitioning into a match, and I was able to do that. My goal is obviously to get inside that top 100."
Teenager Kokkinakis also rose to the occasion as he beat world number 25 Benneteau 6-4 6-3.
The giant 18-year-old fired down nine aces and claimed three of the four break points that came his way to seal an impressive win against the eighth seed.
Kokkinakis said: "I thought a good result like this was just around the corner, [I] had a few tight ones last year where I was up a set on really good players, but [I] wasn't able to finish it.
"So I was happy to keep my composure in the second set."
Kokkinakis will now face compatriot Bernard Tomic, who beat big-serving American Sam Querrey 7-5 7-6 (7-5) at Pat Rafter Arena on a great day for Australian players.
Jeremy Chardy kept the flag flying for France as he saw off Andrey Golubev 6-4 6-4 to reach the last 16.
Rhyne Williams, Denis Kudla, Lukasz Kubot and Marius Copil came through qualifying matches on Monday.