The French Suites, BWV 812–817, are six suites which Johann Sebastian Bach wrote for the clavier between the years of 1722 and 1725. Although Suites Nos. 1 to 4 are typically dated to 1722, it is possible that the first was written somewhat earlier. The suites were later given the name 'French'. Likewise, the English Suites received a later appellation. The name was popularised by Bach's biographer Johann Nikolaus Forkel, who wrote in his 1802 biography of Bach, "One usually calls them French Suites because they are written in the French manner." This claim, however, is inaccurate: like Bach's other suites, they follow a largely Italian convention. There is no surviving definitive manuscript of these suites, and ornamentation varies both in type and in degree across manuscripts. The courantes of the first and third suites are in the French style, the courantes of the other four suites are all in the Italian style. In any case, Bach also employed dance movements that are foreign to the French manner. Usually, the swift second movement after the allemande is named either courante or corrente, but in all these suites the second movements are named courante, according to the Bach catalog listing, which supports the suggestion that these suites are "French". Some of the manuscripts that have come down to us are titled "Suites Pour Le Clavecin", which is what probably led to the tradition of calling them "French" Suites. Two additional suites, one in A minor, the other in E major, are linked to the familiar six in some manuscripts. The Overture in the French style, BWV 831, which Bach published as the second part of Clavier-Übung, is a suite in the French style but not connected to the French suites. Some manuscripts have movements not found in other copies, which are probably spurious.
Suite No. 4 also exists in an alternative version, published as BWV 815a, which includes three additional movements: a Prelude, a second Gavotte and a Menuet.
The first few bars of this suite were written in 1722 for Bach's second wife, but it was not completed until 1723. The Gigue, as often, is in fugal style, in binary form. The voices enter in descending order, while in the second half of the piece the voices not only enter in opposite order but also an inversion of the 1st subject.