The French Suites are thought by musicologists to have been written while Bach was Kappelmeister at the court at Cöthen between 1717 - 1723. Bach did not call these French suites. That is a name that came to be used after his death. Although many of the dances of the suite were popularized in France, the dances themselves came from different parts of Europe, so the suites are not particularly 'French' in style any more than his English Suites are 'English' in style. Later musicologists and editors kept up with the tradition of the names to help differentiate between the three sets of suites.
The standard baroque suite consisted of 4 dances, Allemande, Courante, Sarabande, and Gigue. and could be augmented by other dance types of the era that could be inserted between the standard ones. French Suite No. 5 consists of seven movements, all of which are in binary form and the key of G major:
I. Allemande - Traditionally the first dance in a baroque suite, Allemande is the French translation of the word German. It is in common time and is in a moderately slow tempo. Bach's example here is in gentle, constantly moving sixteenth notes that weave in and out of the parts. As in all baroque music, ornamentation is part of the music, with some ornaments written in the music by the composer. But a performer of the time could also insert other ornaments in the music as long as it was not overdone and was in good taste (a highly subjective thing that was most likely as overdone by some performers in that time as it is by some modern performers.)
II. Courante - A dance of French origin, the courante is a lively dance in triple time. The name itself means running, and this example does that in constant liveliness.
III. Sarabande - A dance of Spanish origin, it is also in triple meter. Thought to have evolved from a livelier (and some sources say an indecent) dance of the 16th century, the dance spread to France where it became a slow courtly dance. The lack of sustained tone of the harpsichord and the slow tempo of the sarabande, caused the sarabande to be more heavily decorated with ornaments to help fill out the music with sound.
IV. Gavotte - An addition to the standard suite, it is a danced of French origin that has four beats to the bar. It is moderate to somewhat faster in tempo, and begins on the 3rd beat of the first bar.
V. Bourrée - Another dance of French origin, it is written in 2 beats to the bar and is usually faster and livelier than the gavotte. It begins on the 2nd or downbeat of the first bar, and Bach's example is full of skips and jumps.
VI. Loure - A slow dance of France, it was also known as the lente gigue, or slow jig. It is characterized by a dotted rhythm and is written in triple time, or as in Bach's example 6/4 time.
VII. Gigue - For the end of this suite Bach uses the last of the four basic dances, the Gigue or Jig, a dance of Irish/English origins. It is a lively dance, and Bach writes it in 12/16 time, which is a compound 2 in a bar meter. It is a 3-voice fugue and the subject is reeled off in sixteenth notes, 6 of them to each beat of the bar: