It may not help that there are more of them, and of course, among themselves they speak Spanish. One of them then turns to me and asks something switching to English, he keeps his speech mostly unchanged (speed, enunciation, pronounciation), except he is putting supposedly English words one after the other...

The Spanish accent in English is --simply put-- atrocious. I've met many Spaniards, and only a few had a clear, understandable accent. Even academics with British or US post-docs may not speak clearly. Nor flight-attendants, for that matter (juecom odi flai tu ásterda).

I only know a few French, but I had a colleague who (although not of the French nationality) was born and raised there, and apparently was taught English literature through reading Les Hauts de Hurlevent. Yes, Wuthering Heights, in French.