The French Revolutionary army was an odd animal. Hodgepodge and haphazard, the Revolutionary army was very different than the previous armies of France. Rather than the restrained, well kept armies dressed in white, the French Revolutionary army was funded and equipped with what they found or given.
The French Revolution and the declaration of the Republic pulled power from the King and placed it in the hands of the people, this included the rights and ability to produce arms. Almost right away, the French Assembly started setting up more foundries and manufactures to produce armaments. Rather than the famed Charleville factory, which made muskets, factories were set up all throughout France to produce hundreds of thousands of muskets
Of course, not all soldiers carried or wore French items. War was the best supplier of arms for the French as they would often take abandoned muskets and artillery guns as well as taking the clothes of the dead or from prisoners. Since the .69 calibre musket was generally the smallest calibre used by European armies, the French didn't need to worry about using different ammunition and often used captured enemy cartridges.
Other units such as members of the national guard would wear their own clothes, being required a blue jacket of a certain style and given a pike if muskets were not available.