Problem with Dreamweaver template site, the css file doesn’t work with Firefox and Chrome

Answers to coding problems are contained in your code. 

My guess:

a) your site is not defined.  Site > New Site...  Links to CSS and other assets are not properly managed by Dreamweaver until you define your site folder.

OR

b) your code contains critical errors that browsers don't understand. Validate code and fix reported errors.   Window > Results > Validation, check document.

Two  questions to better understand your problem :

1 – Did you first define a website ? https://helpx.adobe.com/dreamweaver/how-to/define-a-dreamweaver-site.html

2 – Are you testing localy or remote ?... if remote, did you also upload CSS files ?

If none of them resolve it, please, just send us a screen grab of the HTML code part, where the LINK tag for CSS are displayed.

Plus if you can send a screen grab of the files panel open (LOCAL), that display the files tree