If your traveller taught the Kings' advisors about germ theory, waste-management and the importance of controlling vermin, it could greatly reduce the threat of the various plagues which vexed that age. Taking that idea a step further, convince the King to set up a probationary quarantine policy for immigrants. Finally, teach them how and why they should boil water. A kingdom that knows and obeys these practices will survive and prospherprosper while others sicken and die.
On a different tract, your time-traveller should have some modern musical training and a flute or acoustic guitar. With such tools, some talent and some knowledge of folk tunes and ballads, your traveller can keep themselfthemselves fed, sheltered and safe, regardless of the company he keeps. Such talent is also a wonderful way to get invited to court in the first place.