I agree with your reading of France, as he makes it clear in his last statement you quote from him a more direct opposition to Christ's statement is what he believes it means:
"Yes, it is right, Lord!"
However, the context itself renders France's argument invalid. She is in fact "affirming" Jesus' statement, as is clear from her own qualification. Observe the words used between them, especially the verbs and object of those verbs (taking the ESV quote; lemmas for the Greek words given in brackets):
26 And he answered, “It is not right to take [λαμβάνω] the children's bread [ἄρτος] and
throw [βάλλω] it to the dogs.” 27 She said, “Yes, Lord, yet even the dogs eat
the crumbs [ψιχίον] that fall [πίπτω] from their masters' table.” 28 Then Jesus
answered her, “O woman, great is your faith! Be it done for you as you
desire.” And her daughter was healed instantly. (Matthew 15:26-28,
ESV)
Her counter statement in no way rejects what Christ said. If she was saying "Yes, it is right, Lord!" She would be saying "Yes, it is right, Lord, to take the children's bread and throw it to the dogs." If she were making that statement with her ναί, then her following statement of "the crumbs that fall" would make no sense at all. Who needs falling crumbs if the bread itself is supposed to be taken and tossed to them!?
The problem is France, in this matter anyway, does not see the obvious. Your quote from him notes:
(Davies and Allison, 2:555, declare that "The word is not intended to
contradict Jesus' οὐκ," but give no reason for this surprising
pronouncement.)
Davies and Allison likely give no reason because of the contextual fact (as I demonstrated) that no explanation should be needed. It is not a "surprising announcement" for them to make at all, if one simply considers the context. The woman would not have followed up her ναί with the statement she did make if she intended the ναί to affirm the positive (opposite) of Jesus' negative statement.
France also argues:
The following γὰρ then gives the reason for disagreeing rather than,
as most versions take it, meekly accepting his negative verdict and
pleading for an exception. Surely that would need a following "but" or
"yet," not a "for."
But γὰρ is not always a "reason," for according to William Arndt et. al. in A Greek-English Lexicon of the New Testament and Other Early Christian Literature (Chicago: University of Chicago Press, 2000) [a.k.a. BDAG], while γὰρ is often causal, it can also be a (bold in original):
marker of inference, certainly, by all means, so, then. In self-evident conclusions, esp. in exclamations, strong affirmations, etc.
Because of the γὰρ being the (post-positive) conjunction, the καί in the "καὶ γὰρ" introducing her following statement would be non-conjunctive, and in context, fits as an intensive "even" (BDAG, s.v. καί).
So the Greek and translation would be (note, δὲ and γὰρ are post-positive conjunctions that are placed second in a Greek sentence, but in English, we swap the position of them to the front, so I've grouped those words with braces):
{Ἡ δὲ} εἶπεν Ναί κύριε {καὶ γὰρ} τὰ κυνάρια ἐσθίει
{And she} said, "Yes, Lord, {certainly even} the dogs eat
ἀπὸ τῶν ψιχίων τῶν πιπτόντων ἀπὸ τῆς τραπέζης τῶν κυρίων αὐτῶν
from the crumbs, the ones falling from the table of the Lord of them."
So her statement is an intensifying of her affirmation of Christ's statement, while at the same time offering the further implication that when children are eating their bread (that has not been tossed to the dogs, as Christ said), crumbs fall that the dogs get to partake of themselves.
Her faith was shown in that she believed, as a Gentile, even she could benefit from the leftovers of Christ's ministry to the Jews. He did not have to actively "take" His energy away from His ministry to "give" her enough mercy in healing her daughter (as she asked in v.22, which started the whole encounter). And she was right, Jesus simply spoke it be done and it was (v.28): His ministry to the Jews in no way compromised. But she was rewarded because her faith was such that she knew that she only needed the crumbs of mercy He could show her to heal her daughter.
Commentators
I have yet to find a commentator directly engaging France on this. That is not to say one has not, but perhaps (as I argue above), it is such an obvious thing that she is not contradicting, that commentators have not felt a need. More likely, I just have not found the right commentator.
I have found a couple of commentators so far that do directly engage the concept that France argues for, though without much detail other than a bare assertion.
Stuart K. Weber, Matthew, vol. 1, Holman New Testament Commentary (Nashville, TN: Broadman & Holman Publishers, 2000) on p.232 notes (bold emphasis added):
She worded her response not as a contradiction of what Jesus had just
said but as an extension of the argument Jesus had presented.
Even more remote in the past (1865 for original printing) is John Peter Lange and Philip Schaff, A Commentary on the Holy Scriptures: Matthew (Bellingham, WA: Logos Bible Software, 2008) on page 282 (bold emphasis added; all italics original):
The word ναί by way of admission, not of contradiction; but not
exclusively, or even primarily, referring to the designation “little
dogs.” To have done so would have been to miss the meaning of Christ,
although He had, no doubt, also intended to set before her mind the
defilement clinging to her as a heathen. She acquiesces in the truth
of the whole statement, humbly submitting to the judgment implied in
the figure employed—that she had no right or title to the
covenant-dispensation. But adopting this very figure (not with ἀλλά,
as Chrysostom, Luther, [and our authorized version] have it, but with
καὶγάρ, she converts it into an argument. Yea, Lord—she says—it is
even so: it is not meet to give the children’s bread to the little
dogs; but, on the contrary, the little dogs are sustained by what is
left over from the superabundance on their master’s table. De Wette
interprets: “For dogs must be content with the crumbs which fall from
their master’s table.” The meaning of her reply seems to be: Even so,
Lord; for it is not customary for the children to suffer want in order
that the little dogs may be fed, but rather that the latter are
sustained by the crumbs which fall from the table. Viewed in this
light, the reply is most becoming, indicating: 1. Humility, or
submission to a figure which apparently involved shame and, as
understood by the Jews, reproach. 2. Perseverance, transforming a
seeming refusal into an implied promise of help. 3. Spirituality,
recognizing under the repulsive garb of the figure, the mind of
Christ, whose love and benevolence she realized even through the
unpromising medium. Evidently she beheld the rich fulness of Christ
and of His kingdom. 4. Confidence, that the goodness and grace of the
Lord were unlimited and illimitable.
The fact that these commentators at least mention the contradiction to discount it implies they were at least aware of that idea being circulated for an understanding of it, but apparently not a widely held idea.
Circular Evidence
You note:
R. T. France instead argues that the woman is disagreeing with Jesus.
The NIV2011 is the only translation I could find that follows this
interpretation (a change from the NIV1984 which just says 'yes'.)
The reason for the change in the NIV particularly is no doubt because of France's influence, for according to the Wikipedia article on him:
He had been a member (since 1989; vice-chairman since 2005) of the
Committee on Bible Translation responsible for the New International
Version of the Bible (NIV), and for Today’s New International Version
(2005).
He died in 2012, a year after the 2011 NIV came out. So the NIV translation is not an independent scholarly witness that it should be translated as a contradiction, for France clearly influenced the change.
