I need to move a simple static website from server A to server B (2 different web hosting companies.  I used to use frontpage. Are there apps you'd recommend?

If you are using a basic Frontpage site, my understanding is (and this is from some time ago) that you can move the files, but the server may need to support Frontpage extensions. These were, I believe CGI style scripts. Frontpage ceased to be supported around 2003 and I imagine many hosters would not want a Frontpage site on their server due to potential vulnerabilities. I believe that there is a product called Sharepoint designer, which replaced another Microsoft product. Whether or not this can be used to migrate Frontpage sites I am not sure.

You could try migrating the files using FTP (use SFTP or FTPS, please), and test to see if the site works. If it does, it is likely that Frontpage extensions weren't used. Filezilla is a good FTP client and is quite easy to use.

I strongly suggest updating any site that uses Frontpage. For self-publishing, Wordpress is very popular. I like Joomla. Both are content managed systems and allow you to purchase or use free of charge templates to accelerate production of web sites. Many hosting providers can help you. Some people would also use something like Wix.

The site(s) I'm dealing with now are not frontpage.
Good since finding frontpage hosting is like finding a needle in a haystack these days.

Some constructive feedback would be appreciated here. What about my answer was less than the accepted answer?

Some constructive feedback would be appreciated here

I'd have to agree with Martyn.  He did the lifting, I just supported his post with a link