Courage isn't having the strength to go on - it is going on when you don't have strength.
Comparatively speaking, there are not many things in this world which are impossible. According to the older laws of aerodynamics, the bumblebee cannot fly because its fuselage is too big for its wing area. Fortunately, the bumblebee doesn’t know this; he just flies.
I have the confidence that you will never meet anything you can’t handle. You may not believe this now, but if you will apply all the resources at your disposal, including those within yourself, you will discover it. Courage isn’t having the strength to go on; it’s going on when you don’t have the strength.
(There was a 1967 edition titled Managing Grief Wisely but I was unable to check whether or not it contains the quotation of interest.)
Accordingly I doubt whether Napoléon or Roosevelt said or wrote this. In the case of Napoléon there are volumes and volumes of correspondence and anecdotes, but none of them has anything like the quotation in the post. For example, in Napoléon: ses opinions et jugemens sur les hommes et sur les choses (1838) by Jean-Joseph-Stanislas-Albert Damas-Hinard, the only entries under courage are:
Rien ne donne plus de courage et n’éclaircit plus les idées que de bien connaître la position de son ennemi. (Correspondance de Napoléon avec le ministre de la marine, lettre du 25 mai 1805.)
[Nothing gives more courage or better clarifies ideas than knowing accurately the position of one’s enemy.]
Un homme qui manque de courage n’est pas Français. (Correspondance inédite, officielle et confidentielle de Napoléon Bonaparte, lettre au général Marmont, du 15 frimaire an vii—5 décembre 1798.)
[A man who lacks courage is not French.]