I think that there are a few different concepts being conflated here - let's try to clear those up before getting to the heart of the matter.
First of all, acidity causes just about any dairy product to curdle. That is precisely how cheese is made. Acidity, salt, and heat are all catalysts in the curdling process. This does not, however, affect clarified butter, because curdling is a result of the milk proteins coagulating and binding to each other, and true clarified butter is just the butterfat - there is no milk protein left. Based on that, we can conclude that vinegar is definitely not the important factor, which is further evidenced by the fact that lemon curd will also have a fairly high acidity due to the citric acid in lemon juice.
Crème brûlée is also not heated to 100° C, or even close to it. Dairy products burn very quickly when they approach that temperature. Many recipes for crème brûlée or crème caramel - and IMO virtually all of the good ones - will have you use a bain-marie (water bath) for the express purpose of temperature control. Since egg yolks begin to coagulate at 63° C (145° F), a crème brûlée doesn't need to be heated much higher, although there are many recommendations for the optimal temperature that seem to average around 75° C (around 170° F). If you try boil a crème brûlée, it will almost certainly burn and quite possibly curdle too.
For this reason, I believe that at least part of the difference is simply in your perception of the heat. Ovens heat much more slowly than stoves. Béarnaise (or the very similar Hollandaise) doesn't get heated all the way to 75° C, but it does get heated up to around the 63° C coagulation temperature of egg yolks, which really isn't that far off. You might see the surface of your crème-whatevers sizzle a bit, but that doesn't mean the entire pastries are at the liquid's boiling point; if they were, they'd be ruined.
The rest of the difference is sort of what Bruce's explanation is saying, although I think he's got it backwards, and the reported Julia Child ratio is way off (it should be 2 egg yolks per 3-4 oz of butter, which is only 90-120 mL). The amount of egg yolk (which acts as an emulsifier) relative to fat or dairy is important, but in order for the answer to really make sense, it's also important to understand why.
Egg yolks and butter-fat compose an emulsion of proteins and fat. The fats don't do anything special in response to heat, but the proteins coagulate, and in the process they will try to bind to each other; given a generous enough amount of egg yolk emulsified with butter, if you (a) heat up the yolks past the coagulation temperature and (b) don't keep them extremely well-dispersed, you'll end up with buttery scrambled eggs.
When making crème brûlée - or any custard - you want full coagulation of the egg yolks, because the relatively small amount of protein-packed yolks (typically, anywhere from 10% to 20% of the heavy cream by weight, which is only 4-8% of the fat by weight) is easily dispersed, and the individual molecules can't get close enough to each other to coalesce; instead they form a semi-firm but sparse network around the fat, much like what a meringue does around air.
On the other hand, Béarnaise and Hollandaise are supposed to be sauces. You're trying to thicken but not coagulate the eggs - in other words, allow a very weak protein network to form. To make this partial coagulation have any noticeable effect on the sauce's consistency, you need (relatively speaking) substantially more protein - closer to 30% of the fat. This higher concentration of protein puts the protein molecules in much closer proximity; without constant dispersion (in the form of whisking) and low, slow heat, the proteins will quickly start to coagulate and coalesce, because there's nothing stopping the attraction. This causes flocculation or even outright coalescence of the emulsion, which is the point at which you get that nasty scrambled-egg consistency.
It's got nothing to do with fat:water and everything to do with protein:fat. Fat helps prevent the coagulation of proteins; this principle is applied everywhere including baking, where oil or butter is used to slow down gluten development from flour (not eggs) and keep baked goods from becoming tough and rubbery. The ingredients and cooking method are different in a custard, but the principle is the same.
Protein is the main character in egg-based sauces and in scrambled eggs; the main difference between the two (with custards being somewhere in between) is how much protein, how well dispersed it is, and how much it is allowed to coagulate. Sauces have more protein, less coagulation; custards have less protein with full coagulation.
The difference is not huge, but it's enough to tip the scales if you're not careful.
Best Answer
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.