The Requiem was sung at Chopin’s own request. Then, the Funeral March from his Sonata, Op. 35, and two Preludes were played.
However, there are two versions of how and when the Funeral March was played. One of them is that the Funeral March was also played on the organ, and “was played as the bearers carried the coffin up the aisle of the (Church of) Medeleine”.
The other version is that the Funeral March was played at his graveside after the service at Medeleine by an orchestra in Napoléon Henri Reber’s instrumentation. (It means he rearranged the piece for orchestra from the piano score.)
I am inclined to believing the latter. For one, it is also recorded in Reber’s bio. Also, the two preludes, Op. 28, No. 4 & 6, are some of Chopin’s shortest and simplest. They were short enough for being used as interludes in between parts of the service, and they were simple enough for the organist to get them ready quickly for the performance. On the other hand, the Funeral March is neither as short nor as simple.
Please don’t ask your teacher about this. There are so many of those cute stories around to please the readers. You may easily confirm it on line.