The main house of the Avart Plantation, built in the 1850s, stood at Upperline Street and was bounded by Constance, Laurel and Robert streets. The house no longer existed after 1923, but I can't find details about what happened to it. The Avart Plantation house has been confused with the Ewing House, which was built for Samuel L. Ewing in 1852 and still stands today. What happened to the Avart Plantation house?
The house at 4868 Constance St. is the manor house built in 1853 for Samuel L. Ewing. As you say, it has been confused with the Avart Plantation house, which once stood in an adjacent square across the dividing line between Faubourgs Avart and West Bouligny. The Avart Plantation house was demolished long ago.
The Avarts are perhaps the earliest and most important of Jefferson City's founding families. Robert Avart purchased 17 arpents (a French measurement that equals about 0.85 acres) upriver as early as 1746. His son, Valentin Robert Avart, inherited a share of his father's land in 1773 and over time his holdings grew to 38 arpents. After Valentin's death in 1807, the plantation was divided between his widow and children. Francois Robert Avart, one of Valentin's five sons, made his fortune from a brick yard and lived in a fine country home on his plantation. In October 1841, he subdivided his property, creating Faubourg Avart.
After Francois' death, his wife Amelie Delassize Avart, bought out their children's interest in the estate, and during the 1840s she sold a few lots in Faubourg Avart and built a new residence for herself at what today is Upperline and Laurel streets. The one-and-a-half-story manor house was surrounded by columned galleries and stood within a large orchard of orange, pecan, plum and persimmon trees.
After her death in 1856, the house went to her daughter, Louise Almais. It was demolished in 1923.
The house built for Samuel Ewing was one of the first in the West Bouligny faubourg, and the New Orleans Historic District Landmarks Commission has designated it a local historic landmark.