Not all words mean exactly what they sound like they should mean. Actually, most don’t. But some can be influenced by other words they sound like. Language can be messy that way.
Heck, language can be messy in all sorts of ways. Some words have multiple spellings. Some have multiple pronunciations. Some have both. English is especially that way, thanks to its sloppy history. English is that outfit that looks charmingly raffish in the mirror but downright scuzzy when approached from the side in a grocery store. English wakes up with half its clothes on and isn’t even sure what country it’s in, but it reaches over onto the nightstand and perks itself up with a gulp from the half-empty bottle there and rakes its hair into place with the other hand.
English is frowsy.
Wait, that should be frowzy. No, wait, frousy. Oh, no, look, I’m going with frowsy.
So frowsy has that rhyme of drowsy and blowsy and lousy but not mousey or dozy or boozy. And it opens up with a hint of a frown or a bit of a fringe of something froward. It seems unkempt and heavy-lidded and surrounded by a cloud of flies or cartoon dots and stars.
Well, that’s partly it, anyway. The older sense – from the late 1600s – is of fustiness, mustiness, the fug of the unwashed. By the early 1700s it had spread to ‘dirty, neglected, unkempt’. In other words, Oscar the Grouch or Pigpen from Peanuts. Or that person you hope won’t sit next to you. Or that convenience store you inconvenience yourself to avoid.
So where does this word come from? Um. Sure there’s something we can find under all this matted crap.
No? Hmm. Well, there’s frowsty, meaning ‘fusty, rank’; there’s froughy, ‘musty, stale’, which may or may not be related to frough ‘flimsy, brittle, frail’ and frowish ‘fetid’; there’s frowze ‘frizzy wig’; but for the most part the connections are barely there if at all, and for the most part the etymology can’t be traced farther back than that anyway.
See, English may try to cultivate a James Bond air, or anyway at least some feeling of a louche poet such as Charles Bukowski or Edna St. Vincent Millay, but when it’s at home it’s more like a hoarder with a near-infinity of books and old newspapers, plus thousands of consumer products, including hundreds of bars of soap, every one of them still wrapped and unused and covered in years’ worth of dust. But oh, the stories it can tell… accurate or not… and the stories it can’t manage to tell anymore… Wait, come, sit down, just got out of bed, don’t mind the mess DON’T SIT THERE do you want some of this, that’s better, um, what was it you were wanting to know?
Sesquiotica 
I know. Some of the utter relief at having been born into the English language is that I don’t have to learn it. If you know what I mean.
Hmm. I’m not sure I agree that ‘frowsy’ is a good word to describe the English language. I see English as more of a generous host, one who will squeeze in one more guest at the table, then rush off to the ‘fridge or larder and rustle up another meal. The French, Scandinavians, Romans and Saxons are already making themselves at home. There’s a knock at the door. “Hi” says the American standing there. English thinks for a bit. Yes, we like “hi”. Take a seat. But we’ll draw the line at “howdy”. I’m speaking, of course, of English as spoken in the UK. Americans, as we know, speak American. They say “erbal” instead of “herbal” for instance, presumably due to the influence of the French, who simply ignore any ‘h’ posed at the beginning of a word.
But English also has an impish side. It welcomes in foreign phrases but never promises to pronounce them correctly. Déjà-voo is widely used but not understood by the French, who started it. English also has many pronunciation tricks up its sleeve in the form of regional accents. Any student of English as a foreign language, visiting the UK, hasn’t a hope of understanding anyone in Northumberland, or Somerset, or the whole of Wales, Scotland or Northern Ireland. To name but a few.
So I don’t think English is frowsy, but I haven’t thought of a word that conveys impish hospitality. Yet.