> it sounds like French, flowing from sentence to sentence with the typical melody.

I've heard this described as stress-timed (English) vs syllable-timed (French) languages. Stress-timed meaning the time between stressed syllables is roughly equal, whereas syllable-timed means each syllable is roughly equal length.

You are completely right. Speaking French is actually more than a different set of words, a different grammar and an accent (it probably applies to a lot of other languages). It's also a different mindset. We tend to use a lot of words and expressions to say something that can be summed up in one word in English. Moreover, French people like to speak with images instead of words. So, a word-for-word translation from French to English, which is what most of us do, results in confusing sentences that are hard to follow. Even if I'm a native French speaker, I always have a hard time trying to understand my fellow Frenchies speaking English, but I might be biased...