There is one tool capable of doing precisely what you want: the PlainOldFavorites plugin for Firefox. The author's site describes its intent and function:
Some users still wish to keep some or all their bookmarks in the
Windows Favorites folder. There can be several reasons for this.
First, some new Firefox users might find the transition to Firefox
smoother if they can still use their familiar Favorites folder. Also,
a link to the Favorites folder can be found in several places
throughout Windows, which makes it a convenient option for storing
links. PlainOldFavorites allows using the Favorites folder directly
from Firefox without needing to import or synchronize the bookmarks
Now, the author abandoned development and maintenance of this software in June 2011. The intervening time has seen certain FF revisions which made the program much less compatible (v22 and v29, or so); without updating the code with each rapid-release update, the last release version (v1.4.1) became increasingly unstable and eventually unworkable. The addons.mozilla.org plugin page lists it as incompatible with current FF and does not offer a way to install.
However, in reading the past few dozen interactions in the plugin'suser reviews, it seems some got it to work in versions after FF22, and then again FF29.
INSTALLING: The solution to bypassing the incompatible addons.mozilla.org plugin is to install a slightly earlier release (v1.3.1) directly from the author's website: http://www.iosart.com/firefox/plainoldfavorites/PlainOldFavorites_1.3.1.xpi. Loading the link to this .xpi file in the address bar should initiate installation identically to 'official' addons.mozilla.org plugins.
Now, this is obviously a workaround to a re-implement a piece of code that was technically deprecated 3 years ago. If you want to maintain functionality, you may want to avoid upgrading to new versions of FF, or testing it in a portable FF instance. And I cannot guarantee that this is a stable and permanent solution. That being said, I am testing it in current release v34.0.5, and the plugin's few functions seem to be working.
The plugin creates a Favorites menu in Firefox's menu bar to the right of the Bookmarks menu. (Note that in a fresh install of FFv29+, the menu bar (File, Edit, etc.) is hidden by default. It can be toggled by tapping ALT, or returned permanently.
So the FF bookmark and IE integration exist side-by-side, but their behavior is not synchronized. FF bookmarks do not create IE links, and new IE links do not appear in the FF system. But new IE Favorites do appear instantly in the FF Favorites menu. So, since you want to "replace" the FF bookmark system, you should enable the option in the PlainOldFavorites addon optons to Hide Firefox Bookmarks Menu.
One problem still remains: the CTRL+D keyboard shortcut will send bookmarks to the hidden FF bookmarks. Repurposing the bookmark shortcut key: Download another unsupported addon called KeyConfig (by clicking the Keyconfig link at the top of this post. Restart firefox, and go to the options for the keyconfig addon. Disable all the "Bookmarks..." functions. Then Add a New Key, name it something like Favorites, and replace what's in the code box with
gPofUI.openAddToFavoritesDialog();. Click OK, then hit the key combo CTRL+D n the small text box, and hit the Apply button. Restart firefox again, and now wen you hit CTRL+D, it will open the Add to Favorites dialog window.
With that, you've effectively circumvented the firefox bookmarks system *or at least swept it under the rug), and replaced it with an IE Favorites clone that uses the same data directory as IE (in effect, instant syncrhonization with no 3rd party intermediary).