The EPOCH (EROS-2 periodic variable star classification using machine learning) project aims to detect periodic variable stars in the EROS-2 light curve database. In order to classify these variables, we first build a training set by compiling known variables in the Large Magellanic Could area from the OGLE and MACHO surveys. We crossmatch these variables with the EROS-2 sources and extract 22 variability features from 28,392 light curves of the corresponding EROS-2 sources. We then use Random Forests to classify the EROS-2 sources in the training set. We design the model to separate not only Delta Scuti stars, RR Lyraes, Cepheids, eclipsing binaries and long-period variables, the "superclasses", but also their subclasses, such as RRab, RRc, RRd and RRe for RR Lyraes, and similarly for the other variable types. We apply the trained model to the entire EROS-2 LMC database containing about 29 million sources and find 117,234 periodic variable candidates. Out of these 117,234 periodic variables, 55,285 have not been discovered by either OGLE or MACHO variability studies. This set comprises 1906 Delta Scuti stars, 6,607 RR Lyraes, 638 Cepheids, 178 Type II Cepheids, 34,562 eclipsing binaries and 11,394 long-period variables.