Of course! Arabic has immense influence on Spanish! French had a big influence on English because of 300 years of ruling them(the Normans), and the Moors(Arabic-speakers) ruled Spain for 800 years!
The Spanish word for the, 'El', for example, obviously comes from 'Al'(the in Arabic). Many words. Azul(blue) in Spanish comes from azraq(blue in Arabic), dinero(money) comes from dinar(name for the gold piece in arabic, equivalent of dollar in english), Alcalde(mayor) comes from Al kald, naranja(orange) comes from zaranj, azúcar(sugar) comes al sakkar, algazul(mouthwash) comes from al ghasul, alfajar(a word for a kind of cake) comes from al-fakhur, Albaricoque(apricot) comes from al barquq, alcabala(tax) comes from al qibala, and so on and so on.
Heck, even the name of their capital, Madrid, comes from al Majrit(a word for a soft breeze). Also, there was a dialect which was a mix between Castillian Spanish and Arabic called Mozarabic, which although MOSTLY died out, still has a few speakers in rural Spain and in the former Spanish Morocco. For a period of time, several hundred years actually, everything in Spain was written in Arabic writing, even Castillian. The Moors left behind a lot of architecture. Much of what we consider traditional 'Spanish' archetecture, like Villas, actually come from Arab architectural influence. The traditional Flamingo dance ceoms from Arabic influences as well.
North African Arabic culture specifically has a big influence on Spanish culture. For example in many Spanish-speaking countries, people paint houses blue to ward off the devil. This comes from the North African practice of painting shutters blue for the same purpose.
So in conclusion, if the Moors had not invaded Spain and occupied it, Spanish culture would be DRASTICALLY different today.