Including a PHP file via a function that is part of a plugin?

By creating the above short-code you are trying to call/include entire file wherever [ContactForm] is inserted on your page whereas A short-code is supposed to return a value or output some content.
Since you don’t want a plugin, the best solution I could think of is to create a custom page template. As it’s not a part of your default theme structure so even updating the theme won’t affect it.