Muguruza will meet Estonia's Anett Kontaveit while Raonic will meet Youzhny or Rogerio Dutra Silva.
Reigning French Open champion Garbine Muguruza breezed into the second round on Monday with a straight-sets win over 2010 Roland Garros winner Francesca Schiavone.
Muguruza's middling form this season saw her arrive in Paris with just three wins on clay, but the Spaniard dispatched 36-year-old Schiavone 6-2, 6-4.
The fourth seed will meet Estonia's Anett Kontaveit for a place in round three.
In the men’s competition, Canadian fifth seed Milos Raonic reached the French Open second round on Monday with a 6-3, 6-4, 6-2 win over Steve Darcis of Belgium.
Raonic fired 15 aces and 44 winners and will face either Mikhail Youzhny of Russia or Brazil's Rogerio Dutra Silva for a spot in the last 32.