Overview: The French East India Companies
Strictly speaking the French had three separate monopoly companies. The first, the Compagnie Royale des Indes Orientales, set up by Colbert in 1664, traded only to India, not yet to China and fell into decline over the series of successive wars that marked the end of Louis XIV’s reign: the Franco-Dutch War (1672-78), the War of the League of Augsburg (1688-97), and especially the War of the Spanish Succession (1701-14). As the Company struggled, private trade took over. It was officially permitted albeit Company regulated from 1682 onwards, and it was a private consortium which organised the first successful voyage to China in 1698.
The second company, the Compagnie des Indes, often known as the Law Company, was, as its name suggests, an Indies rather than solely an East Indies Company. It resulted from the 1719 merger, made by John Law of the East Indies, West Indies, and African Companies which, initially at least, also gave the new company lands and trading privileges in Africa, America, and the Indian Ocean. Despite the collapse of the Law Scheme, of which the Company was the backbone, and several reorganisations in the 1720s, the company traded successfully both to India and China for several decades. Having sustained heavy losses first in the War of the Austrian succession (1740-48) and especially in the Seven Years War (1756-63), the company lost its monopoly in 1769.
After 1769 free private trade was thus officially permitted. This ended with the foundation of the third and last monopoly company, known after its instigator, the then Controller General, Calonne, as the Calonne Company. Set up in 1785, the Company lost its exclusive privilege under the Revolution in 1789 but continued to function until 1793.
For further information see Felicia Gottmann, 'French-Asian Connections: The Compagnies des Indes, France's Eastern Trade, and New Directions in Historical Scholarship', The Historical Journal 56 (June 2013), pp. 537-552