Why did my Crème Fraiche split?

Almost all fermented dairy products curdle under heat. When this happens, the milk proteins bind to each other into a rubbery mesh, which can't contain all the moisture from the original product, and it is squeezed out.

Creme fraîche tends to be an exception. It contains a high amount of fat. This fat lubricates the proteins and gets in the way, so they can't bind to each other and form the mesh. However, the fat content of creme fraîche isn't all that high (just enough to allow for the effect I described), so it is finicky when heated.

As you don't seem to have acid in the recipe, the trouble probably comes from water. It dilutes the creme fraîche, making it more probable that proteins will meet and bind without a fat droplet coming in the way. So, if you want to keep the recipe as authentic as possible, try to reduce the amount of water exuded by the other ingredients.

The first thing to check is whether you are actually using creme fraîche. Sometimes people make a substitution with a similar product, but continue calling it the name of the original product. Sour cream, smetana, creme legere, plant substitutes, etc. won't work in your case - 30% fat is the minimum for baking, the higher the fat content, the better is it suited. For the rest of the answer, I am assuming that you are using the creme fraîche.

My suggestion would be to drain the broccoly very well (I assume you mean blanched or nuked broccoli, baking them in the oven would be strange), maybe even try to use a salad dryer. If the salmon comes from a vacuum package, drain it well too, and pat it dry with a paper towel. Take the potatoes out of the boiling pot and leave them alone for a while, the cooling startch will absorb some moisture. Also, use a mealy type of potatoes, the starch in these could absorb some liquid from the other ingredients. Another thing which should help in any case is to reduce the oven temperature, as the gentler heat will affect the creme fraîche less.

If this fails, you should consider adding other ingredients to stabilize the creme fraîche. It will change the taste, but not necessarily for the worse.

A stabilizer should help. For dairy, carrageenan is very effective and its taste is not noticeable, but most people don't have it in the kitchen. Starch will also act as stabilizer, take just a small portion, maybe a teaspoonful per 200 g creme fraîche. Dissolve it in a teaspoonful of cold water before adding it. You could also use flour. Both will affect the taste somewhat, the flour will be more pronounced.

The second solution would be to raise the fat content. Adding pure fat is counterproductive, as the fat droplets in dairy products are much smaller than what your blender would achieve. But you could mix or substitute the creme fraîche using a dairy product with a higher fat content. Mascarpone, kaymak, katuk, clotted cream, or creme double should work. Or maybe cream cheese, even if it doesn't have a higher fat content, because it contains stabilizers. A full substitution will alter the taste substantially, but a partial one will probably be OK.

If all else fails, you could try if you can't change the recipe to accommodate a more traditional gratin liquid (how is the stuff called in English?). While I agree that pure creme fraîche will work best with what you listed, a mixture of eggs (or just yolks to keep it more liquid), milk, the creme fraîche, and a tiny bit of flour would also provide a moist binding. Use less eggs/yolks than in a normal gratin to keep it from setting too much. It will be a big change, but if nothing else works, it will still taste much better than curdled creme fraîche.

Or if you are a risk-embracing nature, you can continue using pure creme fraîche, just with the moisture reducing techniques, hoping that this will be enough. Each time it separates, you should drain the whole dish, catching the liquid. Scum off the curds, or strain them. The whey will have a nice taste, similar to a stock. Take out some new creme fraîche (not heated), and mix it with the liquid. (Reduce it first to avoid making it too liquid). Add it back to the remaining ingredients. This will keep the taste even if the curdling occurs, but will require lots of work.