Grippe, or influenza, is a highly contagious viral disease commonly know today as the flu. Grippe is an old fashioned (and informal) English term, where as influenza is the formal, medical term.
In the Novel Edit
At the beginning of the book, Holden goes to say goodbye to his History teacher, Mr. Spencer, who flunked him. Mr. spencer has the flu and Holden Caulfield uses the old English term, sating that Old Spencer has 'The Grippe'