¿Cuál es tu relación con la lengua inglesa?

[ROBINDESBOIS]

Can we say:
What is your relationship with the English language?
It sounds odd to me. Anything more natural.
I want to ask something like if they study English outside the school, because they speak really well, or if their mother is American or British?

[poli]

Your translation sounds OK, but as you suspect, a little odd. A lot depends on context but maybe I would say:
How did you come to speak English so well?

[Perikles]

I agree with Poli. How about

What contact have you had with the English language?

[Glen]

Or..."What was your connection to the English language?"

[ROBINDESBOIS]

Or what is your connection to the English language I guess? This one fits the purpose.