Explanation:

- Option 1: 1604 A.D.

- Not correct. The French East India Company was not formed at this time.

- Option 2: 1406 A.D.

- Incorrect as well. This date is far too early for the establishment of a European East India Company.

- Option 3: 1664 A.D.

- Correct! The French East India Company was indeed founded in 1664 by Jean-Baptiste Colbert under the reign of Louis XIV to compete with other European trading companies.

- Option 4: 1646 A.D.

- Incorrect. While close to the correct period in history, it is not the founding year.