Why lily of the valley on May 1 ?

On May 1st in France, 60 million lilies of the valley are sold, that is to say 1 sprig of lily of the valley per person!

Mais pourquoi offre t’on du muguet le 1er mai ?

Giving flowers has always been a tradition of pleasure and kindness. In the Middle Ages, the lily of the valley was considered one of the first flowers of spring; and when it was harvested, it was said to "chase away the winter".

During the Renaissance, King Charles IX received a sprig of lily of the valley while visiting the Drôme countryside. 

The king would have kept this tradition with the ladies of the court as a good luck charm for the arrival of spring, then the tradition spread throughout France.

Since May 1st, lily of the valley is offered to wish happiness and luck.

Is there a connection with Labor Day ?

There is no connection, Labor Day is a different tradition in memory of May 1, 1886, when American unions marched to demand that the workday be limited to eight hours a day.
It was on April 24, 1941 that Marshal Pétain established May 1st as "Labor Day".