Final answer:
The French mathematician influential to the Scientific Revolution with his work on analytical geometry was Rene Descartes, who developed mathematical tools that were critical for the advancement of various scientific fields.
Step-by-step explanation:
The French mathematician who also influenced the use of the Scientific Revolution with his work on analytical geometry was Rene Descartes. His contributions to the fields of mathematics, physics, and philosophy were pivotal during the Scientific Revolution. Descartes is known for connecting physical space and reality, observed experimentally, with ideal mathematical concepts, thus bridging the gap between earlier scientific figures like Copernicus and Kepler and later ones such as Newton and Leibniz.
Descartes' work in analytical geometry was fundamental in providing the mathematical tools needed to advance the Scientific Revolution. His method of applying algebra to geometry laid down the groundwork for the development of calculus later by Newton and Leibniz. Descartes' philosophy that embraced doubt and encouraged the questioning of traditional knowledge also contributed significantly to the progress of scientific thought during the Enlightenment.