Notepad++ is a text editor, not a WYSIWYG HTML editor.

Aside from View Current File In that Alan suggested, there are also “preview” plugins available. I use both “Preview HTML” and MarkdownViewer++, both of which will take HTML which is in the active editor tab and display it in a “preview pane” inside Notepad++ (MarkdownViewer++ has the benefit that it also works with Markdown files, and if you set up to use an external X-to-HTML converter, can do other rendered files). Using those plugins is not truly WYSIWYG, but it’s about as close as Notepad++ comes.

The “best” you can do is to tell Notepad++ to run your browser and open the current file. See View menu > View Current File in > …