Do this expression is correct?
[...] a local company, listed on the New York Stock Exchange, willing to penetrate the European market.
That is exactly what I thought you wanted to say, and why I mentioned the point. To be willing to do something is to be ready or to be prepared to do something if you have to. You mean to be eager or keen to do something, which is to wish or want to do it, which is very different. If you still don't understand, send me a PM and I'll explain in French.Sorry but I don't understand well the difference.
My idea is to say that the company wants to penetrate the european market.