In alphabetical order, here's my working list of the top 19:
That leaves one spot for a lot of contenders.
-Borg (6 French Open titles)
-Cochet (5 French Open titles)
-Courier (2 French Open titles, another final, 2 Italian Open titles)
-Djokovic (3 French Open titles, 4 other finals, 6 Italian Open titles, etc.)
-Drobný (2 French Open titles, 3 other finals)
-Kuerten (3 French Open titles)
-Lacoste (3 French Open titles)
-Laver (2 French Opens, made another finals, won the French Pro Championship)
-Lendl (3 French Open titles)
-Nadal (14 French Open titles)
-Nastase (won the French Open w/out dropping a set, 3 Monte Carlo titles, 2 Italian Opens)
-Pietrangeli (2 French Open titles, made 2 other finals, 3 Monte Carlo titles, 2 Italian Opens, German Open)
-Tilden (most clay wins in history, made 43 straight clay finals, 7 U.S. Men's Clay Court Championships [couldn't play at the French Open in his prime])
-Trabert (won the French Open in 1954 & 1955, turned pro, then won the French Pro Championship in 1956 (and 1959))
-Rosewall (2 French Open titles, made another final, 4 French Pro Championships)
-Santana (2 French Open titles; referred to as the greatest clay court player of his generation)
-von Cramm (2 French Open titles, made another final, 6 German Opens, 2 Monte Carlo titles)
-Wilander (3 French Open titles)
-Wilding (won two World Hard Court Championships on clay, 313–13 (96.01%) record on clay, won 120 clay matches in a row [couldn't play at the French Open])
That leaves one spot for a lot of contenders.