Many English dictionaries have more than 300k entries. The reason is that many of the words are close synonyms inherited from different sources. That's what I was trying to get at in my carefully constructed sentence.

IMO the synonyms you link to aren't as close as those at http://www.thesaurus.com/browse/happy - I believe there are further English translations of many of those on your page, but they take things in a different direction. Many of them relate to luck, for example.

I experimented with synonymo.fr a little further. It looks like many distinct English words have a single French word translation, and that French word has different meanings in different contexts. Consequently, looking up the synonyms for that word, you end up seeing synonyms for all the different contextual meanings for that word.

For example, take the word 'sky'. A quick scan seems to suggest French doesn't have distinctly separate words for sky vs heaven, translating both as ciel. Synonymo.fr suggests lots of synonyms, but they are mostly synonyms for heaven, not sky. It's like this with most French words I experimented with; same word, lots of different meanings, where English has separate words without the same degree of "meaning spread". That is, the English words are more precise and less ambiguous. And there are usually more of them, without wandering into different concepts.