Falls are a major risk for elderly people's health and independence. Fast and reliable fall detection systems can improve chances of surviving the accident and coping with its physical and psychological consequences. Recent research has come up with various solutions, all suffering from significant drawbacks, one of them being the intrusiveness into patient's life. This paper proposes a novel fall detection monitoring system based on a sensitive floor sensor made out of a piezoelectric material and a machine learning approach. The detection is done by a combination between a supervised Random Forest and an aggregation of its output over time. The database was made using acquisitions from 28 volunteers simulating falls and other behaviours. Unlike existent fall detection systems, our solution offers the advantages of having a passive sensor (no power supply is needed) and being completely unobtrusive since the sensor comes with the floor. Results are compared with state-of-the-art classification algorithms. On our database, good performance of fall detection was obtained with a True Positive Rate of 94.4% and a False Positive Rate of 2.4%.