Don't rely on Google -- all it tells you is that the word appears on 26,000 web pages; it doesn't tell you whether the word actually exists. If you look at some of the hits for "charmful", it's mostly brand names and such; otherwise, it is a scientific term specific to subatomic physics -- hardly an everyday word.
The word does exist with that definition, but it is effectively obselete and rarely used. Few people know of its existence, and most would consider it wrong. "Charming" gets nearly 54 million hits on Google.
As a matter of fact, Casiopea, Dictionary.com does list "charmful" as an entry in Webster's (and Webster's is a very reputable dictionary).
But that's the problem with dictionaries. Just because they list a particular word does not mean that that word is used or even known by the general public. Dictionaries also list unusual or archaic words which are recognised by people who know lots about language -- but on this site we're more interested in everyday language.
I have a student who uses a dictionary from about 1930. I'll be explaining some word to him, he'll get a puzzled look on his face, open his dictionary and say, "But surely it means this?" Then I have to explain that perhaps it did mean that before the war, but people would give you funny look if you used it in that way now.
Oh, how I can relate, rewboss. Last month, while reading a student's essay, I came across a rather odd sounding 8 syllable noun, or was it 9?, that looked like English but didn't seem to have a single entry in any of the dictionaries I had or had access to. I don't remember the word now, but later, when I had a chance to ask the student about the meaning of the word, he proudly pulled out the dictionary he was using - a somewhat 19th century looking book the size of, well, it could have passed for the NY phone book - and pointed with great joy to the word in question. It was there - in that book. Modern meaning, gymnasium. "It's my grandfather's father's dictionary," he said.
Thanks for all your answers. - Actually, I'd always say "he's a charming person" etc. - I just had the feeling that I had read "charmful" somewhere and wondered why the exercise said that it didn't exist (which seemed even more strange with 26,000 entries in google). But, you convinced me, I won't add it to my active vocabulary .