The four-hour victory over Florin Mergea and Horia Tecau gave France an unbeatable 3-0 lead and secured a last-eight showdown with holders United States in April.
Australian Open finalist Jo-Wilfried Tsonga and world number seven Richard Gasquet won their opening singles on Friday to leave the nine-times champions requiring to win only one of the three remaining rubbers in the three-day tie.
With Clement and Llodra avenging their 2007 first-round defeat by the same Romanian duo on Saturday, the French wrapped up the tie with a day to spare and extended their head-to-head record to 8-1.
"Overall, we played better than last year but the French are top players and Tsonga was extraordinary," Romania captain Florin Segarceanu told reporters.
"We did everything we could."
After taking the first set with ease, Clement and Llodra snapped up the second after the forward charging Romanians were duped by a lucky netcord.
Mergea and Tecau displayed their battling skills when they saved two match points in the third set before securing it 8-6 in the tiebreak.
France were further frustrated when they also dropped the fourth set but charged back in the decider to seal the tie.
Andrei Pavel and Victor Hanescu will be hoping to restore at least some pride for the Romanians in Sunday's dead reverse singles.
(Reporting by Marius Zaharia; editing by Pritha Sarkar)