I'm running CMSimple 3.3, CMSimple LE 3.41, CMSimple_XH 1.2, 1.4.2 and 1.5.2 under PHP 5.3. Everything works fine. But indeed the change to PHP 5.3 might cause the trouble due to some changed settings. And anyway, upgrading to a new version should be best.
I recommend you try CMSimple_XH 1.5.2. The typical way to do the update is to install the new version in a subfolder of the web root and to move the old content.htm, the template folder and the plugins (if any) to the new version. It's best to enter the configuration manually. And you have to convert the old files to UTF-8 without BOM.
If you want to stick with CMSimple 3.3 (I presume you're using a "classic" version -- unfortunately you didn't tell), upgrade documentation is given on: http://www.cmsimple.org/?Installer%27s_Manual:Updating_to_newest