It was Monaco's first home loss of the season and left them second with 41 points from 19 matches, two behind Paris St Germain who host third-placed Lille (39) on Sunday.
Monaco fell behind when their France defender Abidal beat his own goalkeeper Danijel Subasic after the stopper had parried a cross into the path of the former Barcelona player.
The principality team, who were on a five-match winning run, started with Colombia striker Falcao on the bench after a thigh injury had kept him on the sidelines for three weeks.
Falcao eventually came on in the second half but it was Valenciennes who scored again when Ducourtioux beat Subasic from close range at the end of a sharp counter attack.
Rodriguez's goal was too little, too late for Claudio Ranieri's side who were left ruing Falcao's missed penalty.
The result left Valenciennes third from bottom on 14 points but they are now only two points from the safety zone.