BCP stands for "bordereau de communication de pièces". "Pièces" are documents submitted as evidence in a court case, they can also be called "exhibits".

Each party submits a list of the pieces of evidence (exhibits) that they are submitting together with their statements of case (claim, appeal, defence, etc.). This list is the "bordereau".

In your example, "pièce numero 1 du BCP" = document number 1 in the list of exhibits.

Dans la pratique, à chaque fois qu’une partie communique des pièces, l’avocat établit un bordereau de communication de pièce ou BCP, qui liste les pièces transmises.
https://www.isouard-avocat.com/publications/communication-pi...

Here is an example from the UK:
https://www.gov.uk/government/publications/form-pf72-list-of...