Naudain was born near Dover, Delaware and graduated from the College of New Jersey (now Princeton University) in 1806. After graduating from the medical department of the University of Pennsylvania in 1810, he began practicing medicine in Dover, Delaware. After serving as surgeon general of the Delaware Militia during the War of 1812, Naudain was elected to the Delaware House of Representatives from 1823 to 1827, serving as Speaker of the House in 1826.

He was elected by the Delaware legislature to the United States Senate to fill the vacancy left by the resignation of Louis McLane, and was an anti-Jacksonian. Naudain began serving on January 13, 1830. Re-elected to the Senate in 1832, he served as Senator from Delaware until he resigned on June 16, 1836. From 1835 to 1836, Naudain was the Chairman of the Committee on Claims.

Naudain ran for governor of Delaware in 1832 against Caleb P. Bennett, but lost. He served as a member of the board of trustees at Newark College (later the University of Delaware) from 1833 to 1835. An active Presbyterian layman, Naudain proposed that the University decline the proceeds of a state lottery due to the opposition of his church. The state threatened to ask the college to return proceeds purchased from the college's endowment, since they had been financed by an earlier lottery. The board of trustees voted 13-0 againt rejecting the lotter proceeds (Naudain was one of seven trustees who refused to vote), and Naudain resigned his position on the board of trustees.

After serving as senator, Naudain resumed the practice of medicine in Wilmington, Delaware. He returned to the Delaware legislature as a senator from 1836 to 1839. He served as a collector of the port of Wilmington from 1841 to 1845.

Naudain moved to Philadelphia in 1845 to resume medicine. He died in Odessa, Delaware on January 4, 1872.

Naudain was a Freemason, serving at one time as Grand Master of the Grand Lodge of Delaware.