The trouble I have with viewing the whole phrase
fringe benefits not French benefits as one direct object is that
not is an adverb and so must modify a verb, an adjective, or another adverb. I think
not modifies the implicit verb
do get.
I think
fringe benefits and
French benefits are direct objects, but of different clauses:
-We get fringe benefits.
-[We do not get] French benefits. (
We do [not] get is implicit.)
I do not think that
not modifies
French. If that were the intention, I think the sentence would more likely be worded:
We get fringe, non-French benefits.
I would expand your second example,
We ate ten apples not eleven:
-We ate ten apples; we did not eat eleven apples.
I agree that the sentences look and feel different. In the first one, the emphasis is clearly on
ten versus
eleven. In the second sentence, the emphasis is not so clear. To more closely approximate the
meaning of the first sentence, one might have to say:
We ate ten apples and stopped. No one ate the eleventh apple. So the structure "...X not Y" is a convenient shorthand in which the emphasis is quite clear.
But purely grammatically, I think not modifies an implicit verb in a (mostly) implicit second clause.
I would analyze your other examples in the same way:
-Issinbaeva cleared 5.01 meter not 5.02. --- Issinbaeva cleared 5.01 meters; he did not clear 5.02 meters.
-Issinbaeva cleared 5.01 meters, but not 5.02. --- Issinbaeva cleared 5.01 meters, but he did not clear 5.02 meters.
Philip and Anonymous argue that
fringe benefits and
not French benefits are
appositives; i.e., they name or represent the same thing. But the
principal thrust of the sentence is to contrast the two.