The ballet L'Éventail de Jeanne (Jeanne's Fan), composed by ten composers, is considered one of the representative collaborative works of interwar France. Many musicians gathered at Jeanne Dubost's salon in Paris. According to Milhaud, they all contributed pieces as a surprise for Dubost in the spring of 1927, though some sources suggest Dubost commissioned them from the outset. In any case, with its stellar lineup ranging from veterans to promising young talents (Ravel, Ferroud, Ibert, Roland-Manuel, Delannoy, Roussel, Milhaud, Poulenc, Auric, Schmitt), the flourishing salon culture, and its significance in dance history, it is certainly a subject of endless interest from various perspectives. Ravel's Fanfare (for piano four hands) and Poulenc's Pastourelle (for piano solo), among others, are sometimes performed independently.

On June 16, 1927, a small orchestral version, conducted by Roger Désormière, was premiered at Dubost's private residence by the boys and girls of the ballet school she directed. The stage costumes and set designs were created by Dubost's friend, Marie Laurencin. This performance gained renown, leading to a production at the Paris Opéra on March 4, 1929, under the patronage of Jacques Rouché, director of the Opéra. The dancer for Milhaud's Polka was Tamara Toumanova, then 10 years old and hailed as a child prodigy. Toumanova later moved to the United States and achieved worldwide fame as a prima ballerina and film actress.

Milhaud's Polka is in C major, 4/4 time, and in ABA ternary form, consistently employing a diatonic and straightforward compositional style. It is a very light piece, reportedly jotted down one morning in a hotel during his stay in Vienna. Milhaud reportedly found it unamusing that such a salon-style trifle became his debut work at the Opéra, and he did not attend either the rehearsals or the performance. However, as Milhaud habitually underestimated his own works, this statement should not be taken at face value. Its bright and vibrant musical character can be said to enhance the innocent charm of the children and make the dance shine even more brightly.