Simon came away 6-3, 6-3 winner against the number 12 seed and next meets either Argentine Juan Ignacio Chela or American John Isner for a place in the next round.
"I played a good match in difficult windy conditions," said Simon.
"Even if Andy is more at ease on this fast surface, 6-3, 6-3 against him, for me, it's a very good result. I've been playing good tennis for some weeks."
For Roddick it was a second first round clay-court exit in as many weeks after falling a week ago at the Madrid Open.
"He moves very well, which you don't want to see when you are short of matches like I was today, when you are not getting clean hits," said Roddick.
"We soon got into rallies and it became a battle striking the ball in movement, I was coming second sometimes."
Eleventh seed Mardy Fish flew the flag for the US with a 4-6, 6-2, 6-2 victory over Colombia's Santiago Giraldo but there was bad news for Frenchman Gael Monfils who was forced to withdraw from the tournament citing illness.
"I'm not 100 per cent, I don't have any energy," said 10th seed Monfils, who had been due to play Japan's Kel Nishikori in the first round.
"I haven't felt well for a week. I've caught something, I'm not sure what. I'm going to have tests to see what will happen."
Madrid Masters champion Novak Djokovic's next opponent as he bids to extend his victory streak to 35 matches this year will be Poland's Lukasz Kubot, who gained an impressive 7-6 (7-1), 2-6, 6-2 victory over Uruguayan claycourt specialist Pablo Cuevas, who was a semi-finalist at the recent Estoril Open.
France's Jo-Wilfried Tsonga took down Marcos Baghdatis of Cyprus 6-3, 6-2 in an eagerly anticipated first-round clash while Russia's Igor Andreev advanced past Spaniard Pere Riba 6-4, 7-5.
Serbian 15th seed Viktor Troicki ground down Nikolay Davydenko 6-4, 7-5 and Italian Potito Starace defeated Oleksandr Dolgopolov 6-3, 6-3.
-AFPTags: sport, tennis, italy