Copying over the files is unlikely to work.
Remove them and install CC 2014 via your Creative Cloud app instead.
Your subscription includes access to CS6, CC, CC 2014, CC 2015, CC 2015.3, and CC 2017 - all of which can be installed alongside each other, by the way.
The older versions are kind of hidden though - they're not where you think they're going to be. This page covers how to install them.
Thank you very much! Do you know if I will be able to copy over all of my plugins and presets?
Presets and scripts should be able to be copied over without issue. I usually suggest installing plugins rather than copying them over. And that suggestion applies whether you're installing new versions of AE or moving between computers. Things like Form actually install stuff to After Effects (the OBJ importer) that go beyond just the plugin file.
Since you're having to reinstall your plugins anyway, this would be a good time to install the newest version of After Effects too. I find it to be easier to use than CC 2014 and since you're reinstalling plugins anyway, now's a good time to get the latest plugin installers and just install your plugins in both versions. That way, if, for some reason, the new version doesn't work for you, you can always go back to the old one.