It depends
It depends on a lot of things - your goals, your experience, your timeframe, etc.
The majority of game programming isn't language specific. 3D math is 3D math in C# as much as it is in C++. While the APIs may be different, and different 'bookkeeping' may be required, the fundamental logic and math will remain the same.
And it's true that most AAA game engines are C++ with a scripting language on top of them. That is undeniable. However, most AAA engines also have a bunch of in-house tools supporting them, and those may be in anything - Java, C#, C++, etc.
If you want to write a game, and are an experienced developer then C++ and C# have a lot going for them. C# has less housekeeping, while C++ has more available libraries and tools. For anything highly complex, however, you'd be best off trying to use an existing engine as a starting point.
If you want to write a game, and are a new developer then don't write an engine. Use an existing engine, and mod it or use its facilities to write your game. Trust me.
If you want to learn how to write an engine, and are an experienced developer you should probably think about C++. C# is possible as well, but the amount of code and ease of integration of C++ probably puts it over the top.
If you want to learn how to write an engine, and are a new developer I'd probably recommend C#/XNA. You'll get to the game 'stuff' faster, with less headache of learning the ins and outs of C++.
If you want a job in the industry then you need to figure out what kind of job you want. A high-level language can help get a foot in the door dealing with tools and/or web development, which can lead to opportunities on actual game work. Even knowledge of scripting languages can help if you want to go for more of the game designer/scripter position. Chances are that you will not get a job working on core engine stuff immediately, as the skills required to do so are pretty high. Strong C++ development skills are always helpful, especially in real-time or networked scenarios.
AAA game engine development involves some serious brain-twisting code.
If you want to start a professional development house then you probably aren't reading this, but already know that C++ is probably the only viable answer.
If you want to do casual game development then you should probably consider Flash or a similar technology.