Playing in only his sixth grand slam match, Bagnis broke Nadal's serve in the opening game before taking a 2-0 lead.
But if the 99th-ranked Bagnis harboured any hopes of ending the fourth seed's bid for a record-extending 10th Roland Garros title, those dreams were brutally crushed as Nadal surrendered only four further games before wrapping up victory.
Nadal is one of only eight players in the history of men's tennis to reach the 200 grand slam win milestone.
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Beaten in the quarter-finals last year by Novak Djokovic, Nadal has dropped just nine games in two rounds as he attempts to reclaim his title.
He will next play either Frenchman Nicolas Mahut or Marcel Granollers of Spain for a place in the fourth round.
(Reporting by Pritha Sarkar, editing by Martyn Herman)
