I see many questions have been asked about why Napoleon was exiled instead of executed. That is not my question. Rather, why was he given these military forces? I know Metternich predicted in 1814 that Napoleon would be back within two years, but surely you didn't have to be a canny poltician to sense that equipping the man with everything he needed to invade Europe (again) was not a good idea. EDIT: I should add that my source is Jan Swafford's 2014 biography of Beethoven.
It wasn't so much that he was given troops but rather troops came to him. As /u/exostrike mentioned, the support for the Restored Burbon government was shakey. Louis XIII had tried to pretend that the Revolution didn't happen and tried to restore the nobility to their previous state as well as selling the Legion of Honor to whomever was able to pay for it. The latter would make soldiers very unhappy since they held it in high regard. Others like Marshals Ney and Oudinot didn't fit well within the old society, they were too unpolished for the nobility that hadn't seen battle or served the State.
So, when Napoleon came back, people supported him not because of him but because he was better than Louis XVIII. And even those like Davout had rushed to Paris to meet Napoleon.
However, unlike Exostrike, I argue that he would have certainly been able to win but he chose the wrong generals in the wrong places.
truth was he only had an honour guard of 600 men to secure the island that he in effect governed. The royal navy patrolled the island but when they were absent he sneaked across to France.
Poor morale and loyalty to the new regime meant that the troops sent against him propyl changed sides and the state collapsed. Really he shouldn't have been able to win