Great news! 
I finally managed to make the Google Apps work. The main problem is related to signing the binary apks.
The Fairphone needs several precompiled apks, which are located under vendor/qcom/proprietary/target/product/FP2/. Each of them is signed with the normal debug certificate during the build process. The system server (or whatever component is responsible for that) refuses to load those apks during startup. Since some of them need access to the shared user “com.android.system”, they have to be signed with the platform certificate. After i resigned all needed apks, everything seems to be working. At least, the play store is working. 
I wrote two scripts, which shall do the job for you:
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resign-blobs.sh: http://pastebin.com/0eX0u2J6 and the list of apks to resign: http://pastebin.com/YwWb9UpB
Create a bash script and copy the content of the first link to it. Second, create a file calledresign-files.txtfrom the second link. Now, you can resign your apks.
I suppose you are in your Fairphone OS directory. Simple run the script:./resign-blobs.sh. It will resign the apks and copy them to${HOME}/Downloads/fp2. - Create another bash from the content of this link: http://pastebin.com/ZvtP3Yp2
It should be namedinstall-apk-blob.sh. It needs a path to a directory where the resigned apks are located:./install-apk-blob.sh ${HOME}/Downloads/fp2. It will automatically restart adb as root, remount/system, copy the apks and restart adb as non-root.
Cheers,
Alex