Yes, you can try and negotiate the rate (Euribor + X).
You can also negotiate:
Loan to value
Early cancellation fee
Other conditions, such as mortgage insurance.
If you don’t ask, you don’t get.
Be sure to talk to several banks, and let them all know that you are talking to others and will give your business to the best offer. If they think you are a captive client, they won’t make any effort to win your business. It’s the same with any product, in any business. You always have to shop around. Of course this can be a bit more difficult if you don’t speak Spanish and don’t yet live here. In which case, I recommend you use a good broker. A good broker can also use his volume of business to help you get better rates than you could negotiate on your own.