What I'm getting from your description of problem is that you have a website developed in C# and need to test it. If you're thinking of writing tests, using Selenium, then it shouldn't matter which language your website is developed.
You can have a website developed in C# and still use Python/Java code to write Selenium scripts and then test it.
This is one of the best features of this tool.
So you can use the latest version of any IDE (Eclipse, PyCharm), use the Selenium bindings ( Java jars for Eclipse, Python bindings for Pycharm), and start writing your test cases.
So answer to your question :
You can't use C# Selenium bindings in Eclipse, but you can use Java jars in Eclipse, to test your website, which is developed in C#.
However if you want to still use C# to write test cases, then you can use C# bindings in Visual Studio to do so (I think Niels has explained it in detail).