This was exhaustively answered on History.SE question "Was Napoleon as short as “common knowledge” states?Was Napoleon as short as “common knowledge” states?".
I won't provide the complete answer here - you should just read it on History SE - but as we can't close questions as duplicates cross-SE-site, I will offer just one cite from that excellent answer by @coleopterist:
According to the French historian, Marcel Dunan (1963):
"If one refers to the Memoirs of Marchand, t. II, 1955, p.338 "the total height of the crown to heel is 5 feet, 2 inches, 4 lines", or (French measures) 32.47 cm X 5 + 2.7 X 2 + 0.22 X 4 = 1m 68.6.
These measures have been taken by Antonmarchi helped by Marchand. For its part, the No. 8 (January 1963) Bulletin Quarterly information fields of French St. Helena, the Journal of Andrew Darling, English upholsterer who was responsible for taking exact measurements that I am assisted by General Montholon: size 5 feet, 7 inches, or (English measure): 30.47 cm X 5 + 2.54 X 7 = 1m 70.
From these two stories we can conclude that the size of Napoleon was not lower 1m 68.6"
For comparison, the answer offers:
According to this page which cites "Steckel, Richard H. and Roderick Floud (eds.) Health and Welfare during Industrialization Chicago : University of Chicago, 1997" as a source, the average height of a Frenchman between 1800 and 1820 was 164.1 cm.
So, Napoleon was a mite taller than average Frenchman height.