In settings, type "downloads". You should see the option to choose where on your computer you want to automatically save files to.

As shown in the attached image, click on the "Choose" button to select the location.

Do the PDFs auto-open in a new tab, with an address starting with file:/// ?

I can suggest two different fixes, but first, a little background explainer:

Background: inline vs. attachment disposition

If web servers don't specify how Firefox should handle a PDF, or if they specify "inline" handling, then then Firefox loads the PDF as web content with its original URL in the address bar. The PDFs are saved with other cached web content, not in your download folder. This is good.

But web servers can try to force a download by setting Content-Disposition: attachment if they don't want browsers to show the files in a tab. Firefox downloads the file automatically (without asking where to save) and then opens it. Because these are saved to disk the URLs start with file:///. By default, they are saved in your "Save files to" folder on the Settings page.

Two options

(1) Force all PDFs into the web content cache. (This is the setting I use.)

(2) For "attachment" disposition, show the Open/Save/Cancel dialog so you can save the file in your preferred location. (This honors the site's intent to force a save.)

Here's how:

(1) Just for PDFs, override "attachment" disposition to "inline"

When your handling action is "Open in Firefox", all PDFs can now be opened as web content and saved in the cache instead of a regular folder. Here's how you set this up:

(a) In a new tab, type or paste about:config in the address bar and press Enter/Return. Click the button accepting the risk.

More info on about:config: Configuration Editor for Firefox. The moderators would like us to remind you that changes made through this back door aren't fully supported and aren't guaranteed to continue working in the future. I'm using this so I feel comfortable mentioning it.

(b) In the search box in the page, type or paste browser.download.open_pdf_attachments_inline and pause while the list is filtered

(c) Double-click the preference to switch the value from false to true

-- or --

(2) Do not auto-load PDFs with attachment disposition

(a) In a new tab, type or paste about:config in the address bar and press Enter/Return. Click the button accepting the risk.

More info on about:config: Configuration Editor for Firefox. The moderators would like us to remind you that changes made through this back door aren't fully supported and aren't guaranteed to continue working in the future.

(b) In the search box in the page, type or paste browser.download.force_save_internally_handled_attachments and pause while the list is filtered

(c) Double-click the preference to switch the value from false to true

Please note: Firefox probably will be confused if both of these are set to true. I can't remember whether I've tested that.

Hopefully one of those works well for you.