Here's a data point though. Many French students learn in English class, as an anecdote, that "shallow" has no equivalent in French. If there were many other words like this, there would be little point in relating this anecdote. "Shallow" is one of the very few words in English with no French equivalent. French words with no English equivalent? I encounter them all the time.

There are different words for the mouth and leg of an animal versus human. (gueule et patte vs bouche et jambe). There's a common word for the lump of flours that form in dough (grumeau). There's a word for a sandwich with a slice of bread on only one side (tartine). There's a single word for brown sugar (cassonade). There's a different word for hair on your head and hair on your body (cheveux, poils), etc.

Here's a nice list http://www.eupedia.com/europe/missing_words_english.shtml

English words with no French equivalent? Shallow and Serendipity come to mind. I'm googling but I can't find many other at the moment, apart from very technical terms.