The man that Christianity reveres was a middle eastern Jewish Rabbi and as such would have looked much much like the Jews of today's Israel.
They portray Jesus the way they do because historically, Christianity was a European religion and the early Christians wanted to make Jesus appear as someone who would be like themselves.
The popular "image" people have come to accept today of a Caucasian Jesus is the result of the works of the Renaissance painters who were primariy commissioned by the church and the wealthy of that time... which had its base in Europe as mentioned above.
The church had the "final say-so," however, as to how Jesus would consistently look in the frescos and paintings before the famous portrait painters and sculptors of the time would have proceeded.
Jesus was most likely a Caucasian, as he was probably a Semitic person. Semites are a class of the Caucasoid race.