R.Kern and JCOGS Design are correct.
Can you not choose a different name for that template group? You can always use template routes if you need themes as one of your segment names.
You might need to use dynamic="no" in your channel entries tag parameters too.
If you are using EE 3-6 (possibly lower as well) "themes" is a protected name in the EE Installation at the web root of your install. So mydomain.com/themes is seeing that directory before your template directory and throwing the 403 error. Either choose a different name for your template group or do as JCOGS suggested.
EE stores useful CSS and JS resources used by EE itself and some add-ons in the directory /themes - so I imagine any attempt to define a template group with that name will cause problems.
Why your attempts to create a themes.group template folder give you a 403 is unclear to me (rather than some more meaningful error) but suspect that it is EE's way of ...