Murat had betrayed Napoleon in 1814 and had fought against Eugene in Northern Italy. He kept his throne because of it and that was Murat's object.
After 'legitimacy' had returned in 1814 the Neapolitan Bourbons, backed by the French and Spanish Bourbons, began whining for their throne back in Naples. And the Bourbons were demanding military action to oust Murat.
Exelmans had once been Murat's ADC and later his Master of Horse in Naples. He wrote to Murat telling him if the shooting actually started he would gladly come to his old commander's aid, and hinted that he wouldn't be the only one. The letter was allegedly intercepted by someon'e 'intelligent' service. Because France and Naples were at peace, Exelmans had committed no offense, but he most certainly enraged the Bourbons, particularly Berry, and when Soult became Minister of War he had Exelmans arrested, but Exelmans got away and sent in a letter demanding trial by court-martial. He gave himself up to a competent court-martial at Lille and was presently acquitted, adroitly pointing out that the two nations were not at war.
The whole incident had enraged the half-pays put out of the army at the end of the fighting in 1814, many of whom had been replaced by either inexperienced royalists or French officers who had served against France. The army itself was outraged, Exelmans being admired by many young officers, especially light cavalry officers.
What was accomplished was that Soult, maybe purposely, had widened the already growing split between the Bourbons and the French army and he compounded this by expelling the half-pays from Paris. It seems that Soult was playing a game, and keeping it quiet, of raising anger and outrage against the Bourbons, which is one of the reasons his actions as Minister of War were designed to support Napoleon's return in March 1815.