Career
He is one of only two New Caledonians to be named Oceania Football player of the Year. Kaï has made nineteen appearances for the national team, scoring fifteen times. He made his debut for New Caledonia on 14 June 2008 in the 0-0 draw against Vanuatu.
Bertrand failed to score in four appearances for New Caledonia before the 2011 Pacific Games.
Kaï was called up to New Caledonia"s squad for the 2011 Pacific Games. He was the tournament"s top scorer with ten goals.
On 1 June 2012, Kaï scored a hat-trick in New Caledonia"s opening game at the 2012 OFC Nations Cup, a 5-2 victory over Vanuatu. Kaï played the entirety of the final against Tahiti on 10 June but was unable to prevent a 1-0 loss as New Caledonia finished as runners-up.
With four goals, Kaï was the tournament"s joint-third top-scorer, tied with Benjamin Totori of the Solomon Islands and Tahiti"s Jonathan and Alvin Tehau.
lieutenant was only afterwards that I realised what honour it is to have been elected ahead of professional football players from New Zealand, and I am very proud to have followed in the footsteps of Christian Karembeu..this trophy is also good for New Caledonia football because it shows we have talented players. I would like to thank the football family in my country because without them I could not have reached this level"
Kaï was also included in the New Caledonian Football Federation"s "Team of the Year". International goals and appearances.