It's not that easy, as a native french speaking person, I have close to 0 understanding of Italian and Spanish.
I also learned Dutch and English and those two are much closer.
I think you underestimate the similarities with Italian and Spanish, and overestimate the similarities of Dutch and English because it's easier to notice similarities when you're looking at two foreign languages where it's the similarities that will stand out, than when looking "closer to home" where the differences tends to stand out.
Though Dutch and English are really quite similar, they're not all that much closer related than e.g. French and Spanish.
During my French-lessons, my French teacher often used Spanish (which none of us knew) as a means of explaining French vocabulary for us by means of demonstrating the transitions in sounds from the latin origins of both, and the same works between French and Portuguese, Italian, Romanian, as well as with many languages further removed from latin that still has plenty of loan words. The same also does work between English and French because of the number of French and latin words in English, but much less so between the other Germanic languages and French.
E.g. try to go to www.repubblica.it (a random Italian paper) and cut and paste a paragraph or two into Google translate with French as the target, and look at how many words are similar. Then try to change the target to e.g. Dutch or German, and you'll see far fewer similarities. Switch to English and you'll tend to find something a bit in the middle.
It does vary a lot - more formal texts tend to be more similar. I can pretty much straight up read very formal Italian by picking up context, based on French + knowing a handful of other Italian words, but I'd certainly find it much harder to read casual comments.
French is really different from Italian, Spanish and Portugese. Or even Romanian. If you know Spanish you kind of get the idea of what people write in the other four languages.
But I think you get a lot of English during your life if you live in Europe which makes it easier for you to pick it up. There are still more Latin derived words in English than French derived, Spanifying English words is not a bad strategy if you're learning to speak Spanish and you have a feel for Latin sounding words in English.
Dutch? Perhaps if you're Belgian? Not so much overlap with French even though there are influences.
