On 26 March 1849, Caverot was appointed Bishop of Saint-Dié, he received his episcopal consecration on 22 July and was installed on 5 August.

When the railway arrived in 1864, he acquired and saved the chapel of Petit-Saint-Dié, believed to be a seventh-century place of Christian worship.

He participated in the First Vatican Council in 1870 and voted in favor of papal infallibility.

[1] In Lyon, he reorganized the diocesan administration and worked to support Catholic education at all levels in light of the laws of 1881.

In 1885, he urged Catholics not to attend performances of Jules Massenet's opera Herodiade, for which a 21st-century musicologist labels him a "reactionary cleric".