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Having gone out in the first round at the Australian Open earlier this month, former world number one Muguruza did the same in France, suffering a resounding 6-1 6-4 defeat to 18-year-old Czech qualifier Noskova.
Third seed Cornet did not fare much better on home soil, capitulating after drawing level with Osorio as the Colombian triumphed 6-4 4-6 6-1.
The other seeds in action on day one at the WTA 250 event avoided the same fate, with fifth seed Anastasia Potapova beating Marina Bassols Ribera 4-6 6-1 6-2 and fourth seed Petra Martic fighting back to edge her two-hour battle with Kristina Mladenovic 3-6 6-3 7-5.
At the Thailand Open in Hua Hin, third seed Wang Xiyu was beaten in an all-Chinese meeting with Zhu Lin, while Wang Xinyu triumphed in straight sets against Joanne Zuger and Ukraine's Lesia Tsurenko eliminated Ysaline Bonaventure.
