Only three matches were completed in the morning before the weather stopped any further play and 21 matches, including six first round singles, are scheduled for Wednesday.
Jones, the first local qualifier to make the first round of the tournament since 1979, battled gamely but produced too many unforced errors against claycourt specialist Massu, who was a former top-10 player.
Massu broke in the ninth game of the first set, then twice again in the second to run out a comfortable winner.
He will meet the winner of the match between Finland's 2006 champion Jarkko Nieminen and Belgium's Xavier Malisse.
Seventh-seeded German Philipp Kohlschreiber also managed to avoid the wet weather and converted all five break points he created to beat Michael Russell of the U.S. 7-5 6-2, while Argentine Sergio Roitman beat Czech Lukas Rosol 6-2 7-5. (Reporting by Greg Stutchbury in Melbourne; Editing by Alison Wildey)
