Grobon was a pupil of Bonnefond at the School of Fine Arts in Lyon from 1831 to 1836 and of Victor Orsel. He exhibited in Lyon from 1836 and in Paris from 1842. Around 1863, he settled in Paris where he painted on porcelain and decorated the chapel of the Oratory. He also produces lithographs, either with his brother Anthelme Eugène Grobon, or alone.
Grobon draws, in Lyon, a series of portraits (engravings and lithographs) including Flachat and P. Bendois, actors; B. Gingène and Louise Labé, in the style of Foyatier.