Little is known about his early life, and he first appears in the records as a singer to Isabella de Bourbon, who was the wife of Charles the Bold. Later he seems to have joined the personal chapel of Charles, when Charles became Duke. Unlike many of the musicians of the Burgundian court, who traveled along with Charles on his military exploits (who loved music as much as war, and enjoyed having musical entertainment during his military adventures), Basin seems to have remained in Bruges most of the time. After the death of Charles at the Battle of Nancy in 1477, Basin served the court as a diplomat, according to records from the 1480s. The last record of his life is dated to 1498, when he was named as heir to his brother Pierre.
All of Basin's surviving music is secular, although some of the anonymous music in the manuscripts of the time may be by him. Of his secular songs, one became immensely popular. Nos amys vous vous abusés was used by several later composers, including Tinctoris, as a source for mass settings, and numerous copies of the song have been found, some in collections as far away as Poland and Portugal. Before the advent of music printing at the beginning of the 16th century, such distribution is rare, and generally shows the popularity of a piece.
Dates of composition of Basin's songs are not known, but probably they were written during the period when he was a singer for Charles. If he wrote later music, either it has not survived, or has survived anonymously.