I'm not familiar with camera traps, but there are a couple of options:
1) If the animals tend to cover most part of the image, then you can train a CNN classifier to distinguish between species (available with the keras-Tensorflow modules in Python)
2) If, however, the animals only cover a small part of the image (e.g. in the distance), it might be better to use an object detector (I've used YOLOv2 in the past for fish detection), which however is not that straightforward, especially with Python (I used MATLAB)
In any case, keras-Tensorflow classification with Python might be the most straightforward option for your goal. You should also certainly have a look at Google's Wildlife Insights platform which is specialized for species classification from camera trap images.