Heat the olive oil in a large casserole. Saute the onions in the olive oil for about 5 minutes or until softened. Add tomatoes, broth, wine, garlic, bouquet garni and saffron. Bring to a simmer. Add potatoes, carrots and chicken, season to taste with salt and pepper. Bring the soup back to a simmer, cover the pan and simmer gently just until the chicken and vegetables are cooked through, about 45 minutes.
While this is cooking through, make the rouille which accompanies it.
Note that potatoes freeze badly. If you are making this in a double batch in advance and want to freeze it, make it without the potatoes and simmer broth for 40 minutes only or until carrots are tender and chicken is done. If you are serving half the recipe that night, cook some potatoes separately and add them to the soup later. Freeze leftovers and on day of reheating it, cook potatoes separately and add to a broth after it is reheated.