In 1981, Carlos Matamoros Franco won the bronze medal at the World Youth Chess Championship in the U16 age group.
In 2005, he participated in the Chess World Cup but lost to Victor Bologan in the first round.
In 2008, Carlos Matamoros Franco, along with Martha Fierro, won the gold medal at the World Mind Sports Games in the Mixed Pairs Blitz event.
Carlos Matamoros Franco has played for Ecuador in the Chess Olympiads many times:[2] Carlos Matamoros Franco played for Ecuador on board one at the 2003 Pan American Team Chess Championship in Rio de Janeiro (+2, =0, -1) and won the team bronze and individual gold medals.
[5] Carlos Matamoros Franco played for Ecuador in the World Youth U26 Team Chess Championship:[6] In 1987, he was awarded the FIDE International Master (IM) title and in 2002 he received the FIDE Grandmaster (GM) title.