Reports from Wallis say supporters of the King have lifted a series of roadblocks after reaching an agreement with a mediator in their dispute with a rival clan.
Television New Caledonia reports the mediator, Louis Lefranc, as saying that France has agreed to recognise the Lavelua Tomasi Kulimoetoke as the only king of Wallis.
A clan described as pro-reform and pro-French announced it would crown a new king last Sunday.
This prompted supporters of the king, the Lavelua, to block key roads and damage the airstrip to prevent extra French police from being flown in.
Some of the men at the barricades were described as armed.
A clash on Friday left one person injured, schools have been closed for days and public servants have been told to stay ay home.
In May the Lavelua challenged the French judicial authorities and asked them to leave the island.
In 1961, the Lavelua signed the agreement that saw Wallis become a French territory.