Do breads always have to be baked in some vessels in an oven? If yes, then what shaped vessels would those be?

The general answer is that you use a loaf pan if you want the common rectangular loaf shape (it's good for slicing for toast and sandwiches), and otherwise you don't need one.

For example, the link you gave for french bread completely describes how to shape and bake the loaf. There's no wrapping in foil or anything; you coax it into that shape, and it's flexible and stretchy but won't spread out or anything. I'm not sure why it refers to a "baking vessel", implying that it's something that contains the loaf. All you need is a flat baking sheet.

Once you've made bread dough this should be pretty obvious - it's not a big wet mess, it's something with structure that you can work with and shape. It's pretty much the same with all other shapes of loaves - you get them into the general shape, toss them on a baking sheet, and bake them. You can make small circular rolls, small oblong rolls, big circular loaves, big oblong loaves, whatever suits you. There are certainly traditional shapes for some breads, and you should probably follow recipes, since baking times are of course affected by size, but the general principle remains the same - you shape it how you want it.

After taking a glimpse at the website, I think I know what she is talking about.

I keep my pizza stone in the oven at all times. I bake my bread directly on top of it. I makes for even baking, and a wonderful crust on the bottom. The same principle applies with a Cast Iron Dutch Oven. I'm assuming that she is talking about the type you would use camping, over a campfire, that are massive. You would put your bread inside of that "vessel."

That being said - You can bake French Bread without one of these things. The crust won't end up the same, but it is worth taking a chance.

However, I really suggest getting a pizza stone. They can be found rather inexpensively, and they really improve many different breads. I put either my loaf pans or baking sheets directly atop the pizza stone. Another plus I've found with the pizza stone, is that it keeps the heat of the oven better distributed. It is well worth the investment.

Sometimes the vessel serves other purposes besides shaping. For example, in the book I'm currently working through, Tartine Bread, they suggest baking the shaped loaves inside a dutch oven to increase the humidity of the air immediately next to the bread -- the dutch oven will capture escaping steam and hold it near the bread, resulting in a better loaf. This appears to be the same theory espoused in your link.

Where I come from (Switzerland) it is indeed very uncommon to use any vessel. Indeed the various shapes of bread even set them apart. You can image-google for "Butterzopf", "Krustenkranz", or just plain "brot" to get an inspiration if you feel like baking a shaped bread.