Baugin was born in Pithiviers to a prosperous family. He received his artistic training from 1622 to 1628, and entered the guild of St.-Germaine-des-Prés as a master painter on May 23, 1629. Around 1632–3he traveled to Italy, where he settled in Rome. After 1641 he worked in Paris.
With one exception, his surviving subject pictures are religious works, including numerous small paintings representing the Virgin and Child or the Holy Family. No painted portraits by his hand are known to have survived, although several are known through engravings. He has also been credited with a group of four still lifes. None of his works are dated.
He died in Paris.