Yep, that's how I hear it, too; nothing like what I think of as a spoken, simple "schwa." The dictionary entries show the schwa, but it's a pretty lousy signifier, in my opinion - if simply reading the dictionary, non-speakers would, I think, be led to conclude the simple "Tom," or "tum", 'mericanese. Here's some other schwas in action:
Schwa
The schwa is the vowel sound in many lightly pronounced unaccented syllables in words of more than one syllable. It is sometimes signified by the pronunciation "uh" or symbolized by an upside-down rotated e.
A schwa sound can be represented by any vowel. In most dialects, for example, the schwa sound is found in the following words:
The a is schwa in adept.
The e is schwa in synthesis.
The i is schwa in decimal.
The o is schwa in harmony.
The u is schwa in medium.
The y is schwa in syringe.
Authorities vary somewhat in the range of what is considered a schwa sound, but the above examples are generally accepted.
Some browser fonts will show the schwa symbol here: ə. Others may show either a box, a question mark, or capital Y.
Doesn't quite seal up the debate. Now - to make matters worse, "tomme" is a single syllable; not a "throw away," unaccented syllable, as in a-way.
In spoken French, my ear has always heard that edge of long "o" as a slight hybrid, joining the short or "schwa."
I think when one puts the two words "tomme" and "Tom" together, the difference should be heard. Helen, you're the native - does it sounds like a simple "Tom" to you?
(There's no money riding on this. Just my ability to sleep tonight).
Edit: Actually, what I'm saying is in the Larousse site: two words, supposedly identical phonetics:
Tom (name - acronym, but the meaning's illustrative) : tɔm.
Pronounciation.
tomme, the cheese: tɔm.
Pronunciation.
Identical phonetic spelling; quite different, in my opinion, in spoken language.
I now pour my Fleurie, sink into some Stendhal, and sleep like a baby lamb.