Meunier was born on 4 August 1770 to a family of modest means in Saint-Amour in what later became the Jura department. He enlisted in the 10th Jura Volunteer Battalion on 5 August 1792 and became a captain seven days later. He fought with the Army of the Rhine from 1792 to 1794. He was wounded in the left thigh by a bullet on 13 October 1793 at the First Battle of Wissembourg. He transferred to the Army of Italy where he served from 1794 to 1797. On 14 May 1797 Meunier was a grenadier captain in the 1st Battalion of the 69th Demi-Brigade. He transferred to the Army of the Orient and fought in the French campaign in Egypt and Syria in 1798–1801. He became captain in the Foot Guides on 20 January 1799 and was promoted to "chef de bataillon" (major) on 17 February 1800.