The easiest way is probably to make a system call to a Python script that writes the predictions to a binary or HDF5 file, which can be read in from C++. You can also directly integrate Python into C++.
If you need to deploy and distribute this easily, you can look into self-contained Python installations like Anaconda, but your best bet may be to avoid Keras and use the C++ interface to Caffe or Tensorflow. I wouldn't recommend Tensorflow since using it from C++ isn't standard; see this discussion. Caffe is arguably the second most-popular deep learning library so you can't really go wrong.
