Davout was prepared to 'accept' the Bourbons because he had no choice. However, he did not serve them, was falsely accused by them of financial inproprieties in Hamburg during the siege, and was rebuffed by them upon his return from Germany in 1814.
I don't see any evidence that he willingly wished to serve them, or that he took an oath to them. The Bourbons could not prosecute Davout in 1815 because of those facts.
Please refer to John Gallagher's The Iron Marshal, pages 296-297. In point of fact, reading the entire volume might be helpful.