Complex sentence: The English flageolet never reached the level of popularity that the "French" flageolet enjoyed in the 19th century, which was in use until the beginning of the 20th century, when it declined in popularity.
Split into simpler sentences: The English flageolet never reached the level of popularity that the "French" flageolet enjoyed in the 19th century. Both were in use until the beginning of the 20th century, when they declined in popularity.