The first U.S. census in Louisiana was in 1810 (LA had been purchased in 1803). Here are the indices for the HEBERT's in the first seven federal censuses.
HEBERT's in the 1810 Census of Louisiana
HEBERT's in the 1820 Census of Louisiana
HEBERT's in the 1830 Census of Louisiana
HEBERT's in the 1840 Census of Louisiana
HEBERT's in the 1850 Census of Louisiana
HEBERT's in the 1860 Census of Louisiana
HEBERT's in the 1870 Census of Louisiana