Many people report with CM12 (such as FatToad on my wife and my Samsung T699 Relax. We like keyboards) that Google Play (services) stops and starts.

http://forum.cyanogenmod.org/topic/103620-cm12-unfortunately-google-play-services-has-stopped/

has this to say about it:

ATTENTION: To all those having trouble with Gapps crashing on CM12, there
is a solution. It is not the fault of the CM or the Gapps. Simply
updating the Custom Recovery is what fixes the problem as this is a
permissions related issue. After that you can install any Gapps
package. After hours of digging on the net, I came across this solution
and I can confirm it works 100%.

You can download the latest Recovery mod by searching the net. I don't
have any posts to my name so I can't share outside links. The version I used was
openrecovery-twrp-2.8.5.2-mako

The best part is that you don't even have to wait to boot to copy stuff
back to the internal storage, as the latest version comes with MTP
support directly from the Recovery mode itself. Simply brilliant.

The only point to remember is that after updating your Recovery, please
fix the root settings if it asks you and then do a clean install all over
again, including the CM12 image. And this time your Gapps installation
will boot smoothly too.

I am using clockworkmodrecovery.6045.apexqtmo.touch.img, which I have put here: http://junk.sandelman.ca/junk/r2s3/

I found that recovery-clockwork-6.0.4.4 did not work: not sure why see below. I also wound up with a few dud downloads of 6.0.4.5. I also put a subdir T699, which contains the original firmware for the S Relax, as you might need that if you have to SIM unlock it.

Remember the WIPE THE CACHE after you update stuff like this.

Also see: http://androidpulp.blogspot.com/2014/09/cwm-6045-recovery-for-galaxy-s-relay-4g.html

I also note that I tried multiple times using both “adb sideload” for the gapps-lp, and also finally I did it again with a regular

and used the regular install zip from zip. After this attempt, the dalvik optimization stage (“Android is upgrading”…) took a lot longer, with 117 apps to “optimize”.

Some of these suggestions might also help you:

http://www.teamandroid.com/2015/04/22/fix-google-play-services-has-stopped-error-message/