chmod() operation not permitted - FatFree framework

For this you have to give the permissions recursively using -R for your "webapp" folder

Siddharth alludes to the correct answer in the comments:

F3 compiles templates to a temp/ dir before serving. This temp dir needs to a) exist and b) have appropriate permissions.

To achieve this, go the dir where your template file exists and run:

mkdir temp/
chown www-data temp

Check intermediary directories permissions It's a common gotcha.