Does creme fraiche contain live bacteria in the same way that yoghurt does?

Unfortunately, I can only give a similar answer to ones you've received in your question about sour cream -- generally, you'll have to contact the manufacturer.

That said, most commercial cultured dairy products do not undergo a second "pasteurization" step after fermentation, and in a few searches on the topic, I wasn't able to find anything about crème fraîche manufacture that would indicate that pasteurization after culturing is common. Even yogurt that is "heat treated" after fermentation is often not subjected to the same levels of heat and time that would be required for normal pasteurization -- thus, while some (and maybe most) bacteria may be killed off, it's likely that some remain.

I would generally assume that any cultured dairy product (crème fraîche, yogurt, cultured buttermilk, kefir, sour cream, etc.) will contain at least some live bacteria unless the label or manufacturer explicitly tells you otherwise. The question is the concentration. Usually high-fat cultured dairy products (crème fraîche, sour cream) contain a lower concentration of culturing bacteria than lower fat dairy (yogurt, buttermilk), but it's tough to know how low.

Regardless, "full-fat" crème fraîche should generally be relatively stable even if you heat it. So, you could theoretically pasteurize it yourself by heating above 150F (66C) for at least 30 minutes. At higher temperatures, pasteurization will take less time (the standard for commercial pasteurization of high-fat milk products is usually 15 seconds at 166F (74C)), though at some point you'll begin significantly altering the texture of the product at high temperature.

Keep in mind, though, that even "pasteurized" products usually contain small amounts of active lactic-acid bacteria. Pasteurization temperatures and time are designed around killing specific nasty bacteria which are known to cause illness. The kind of bacteria used for culturing dairy products are not generally considered harmful, and many of them can survive longer at high temperatures (hence, the reason why pasteurized milk eventually often "goes sour"). If you're looking for dairy products that are actually sterile (with no live bacteria), you'll need to look at "ultra-high temperature" (UHT) pasteurized products. These are the sort of dairy products that can often be stored on the shelf without refrigeration for months without going bad. Normal "pasteurized" dairy products still should be expected to contain some live bacteria (just a lower concentration), which is why they are refrigerated.