Do you mean the "Refresh" feature described in this article: Refresh Firefox - reset add-ons and settings?

That feature is supposed to automatically migrate your bookmarks. Your old bookmark backups should be in a folder on your desktop called Old Firefox Data. Can you find that?

If yes, return to the Library window, Restore menu, click Choose File, and point Firefox up to the desktop and down into Old Firefox Data, into the semi-randomly named profile folder (example: a1b2c3d4.default), and into the bookmarkbackups folder and try to restore the most recent of those.

Does it work?

You can check if you have an "Old Firefox Data" folder on the desktop in case the Refresh feature in Firefox has been used and a new profile has been created.

You can copy files like these with Firefox closed to the current profile folder to recover specific data.

• bookmarks and history: places.sqlite
• bookmark backups: compressed .jsonlz4 JSON backups in the bookmarkbackups folder
• cookies.sqlite for the Cookies
• formhistory.sqlite for saved autocomplete Form Data
• logins.json (passwords) and key4.db (58+) or key3.db (57 and older) (decryption key) for Passwords saved in the Password Manager
  if you only have key3.db then make sure to remove an existing key4.db
• cert9.db (58+) or cert8.db (57 and older) for (intermediate) certificates stored in the Certificate Manager
  if you only have cert8.db then make sure to remove an existing cert9.db
• persdict.dat for words you added to the spelling checker dictionary
• permissions.sqlite for Permissions and possibly content-prefs.sqlite for other website specific data (Site Preferences)
• sessionstore.jsonlz4 for open tabs and pinned tabs (see also the sessionstore-backups folder)

See also:

• https://support.mozilla.org/en-US/kb/recovering-important-data-from-an-old-profile