Standard French certainly has no lexical stress, but it does have stressed phrase groups and uses contrastive stress. As the last syllable of a French phrase group is given a falling pitch and drawn out pronunciation, polysyllabic words spoken in isolation sound as if they all have a slight stress on the final syllable.
The everyday spoken language is a different story. At least in the regional variety I am familiar with (Genevese French), you can hear word stress. I don't know if this follows much of a pattern or to what extent it varies between speakers but I can at least give one somewhat weak example: some speakers pronounce a final 'e' as in 'pomme', but the accent remains on the first syllable.
As for other languages which lack word stress, Taiwanese Mandarin and Japanese come to mind. The tones in Mandarin and the pitch-accent in Japanese seem to be incompatible with lexical stress, unless you take a rather broad definition of lexical stress. (I write Taiwanese Mandarin because in Beijing Mandarin there seems to be a trend towards word stress, but for now it is explained using a special 'neutral tone'.)
I too would be interested to learn of another example of a non-tonal language that lacks lexical stress.