You need to specify .html as an extension to the AddHandler specification.
AddHandler application/x-httpd-php-source .html
Or you could use a FilesMatch block to set the handler.
There appear to be two handlers for php:
application/x-httpd-php-source. Check you configuration to see which is being used when
.php files are processed.
An alternative would be to do internal redirects from
.php such as:
RewriteRule (.*).html $1.php
You can make his conditional on the .html page not existing. The files would need to be renamed accordingly.
Unless you block or externally redirect .php URLs, requests for .php pages will work. This kind of redirection can be difficult.