First of all, you can keep using FP, but you will need to use FTP uploading, instead of Front Page Extensions. Go to your webhost knowledge base to learn how to upload your site using FTP. They may even specifically talk about Front Page and Front Page Extensions.
FileZilla is a good, free FTP program. There are also good instructions on how to use it here:
https://filezilla-project.org/
Moving to Expression Web is a viable option for you, but realize that the learning curve is huge compared to FP. EW is a professional, fully standards compliant web making tool. Here is the EW forum link where you can ask questions, but fair warning, these
experts aren't always the most patient. https://social.msdn.microsoft.com/Forums/expression/en-US/home?forum=web
You might want to read this particular post: https://social.msdn.microsoft.com/Forums/expression/en-US/d0ef49b5-1619-47b4-812b-ae14efd24e51/frontpage-extensions?forum=web
While looking up the EW forum link, I ran across a couple other links that you might find interesting. In fact you might want to Google 'FrontPage to Expression Web' for more.
https://www.expression-web-tutorials.com/resources.html
There is lots of good help if you go to EW, but also a link specifically for moving from FP to EW. You will have to pay for the book though.
Another site (don't know how good it is) http://www.prorganize.com/help/pages/frontpage-conversion-help.html
Again, if you are willing to put a lot of work into learning how to use EW and probably totally change your current website, then go for it. FP is not a standards compliant program and that is part of the reason why it was dropped after FP2003, but you still
see simple websites built with FP. In fact I have seen Office MVPs that use it.
I suspect you should investigate and learn how to use FTP to upload your FP site and save a lot of time and work. In fact after writing all of this I googled the subject and found a list of articles that describe just that. Again, I would go your webhost
knowlege base or help section and they will probably have specific instructions on how to do this, but you might find these helpful too:
https://www.google.com/search?q=frontpage+ftp&ie=utf-8&oe=utf-8&client=firefox-b-1
DavidF