Put the beef, onion, carrots, garlic and bouquet garni in a large bowl. Add the wine. Using your hands, mix all the ingredients together, then cover the bowl with plastic wrap and refrigerate for 24 hours.
Remove the beef from the marinade, reserving 2 cups of the liquid, and dry the meat well on paper towels,
Fry the bacon in a large pot over medium heat until crisp, about 7 minutes. Season the beef with salt and pepper. Add it to the pot and brown it on all sides, about 7 minutes. Sprinkle with the flour and cook, stirring constatly for 3 minutes. Add the reserved marinade, vegetables, 3 cups of beef broth and 2 cups of water and bring them to a boil over high heat, scraping up any brown bits. Reduce the heat to low, cover and cook until the meat is tender, about 3 hours.
Add the mushrooms and cook for 30 minutes longer until the mushrooms are tender. Remove the bouquet garni before serving.
NOTES: If you can't get a bouquet garni in the store, you can make your own with 1 sprig fresh thyme, 1 bay leaf, 4 sprigs fresh parsley, 1 spring fresh tarragon (optional) and 4 peppercorns. Wrap it all up in a bundle of cheesecloth and tie closed with kitchen string – leave the string long to tie to the handle of the pot to make it easy to remove.