Since I guessed E when I read this question, and since the GRE is all about guessing which answer the test deviser has decided is the right one, perhaps my analysis in settling on answer E will be of some value to you.
First, we need to nail down precisely what the author's contention and evidence are. The author's core contention is that the French are very fond of junk food, and the author's evidence for this contention is that Paris has more burger & fries restaurants than any other European capital city.
There are a number of ways to challenge the logical connection between the presence in Paris of many burger & fries joints and the supposed love of the French for junk food. One might be that burger & fries joints exist only in Paris and not in the rest of France, which would tend to indicate that, at most, Parisians love junk food but the rest of the French does not. But none of the options offer counterevidence of this type. Let's look at the types of counterevidence that are offered.
A. There are also a larger number of Lebanese restaurants in Paris than there are in other European capital cities
One possibility is that Paris has more restaurants of every kind than any other European capital. In that case, the large number of burger & fries joints becomes less compelling as proof that the French have a special fondness for junk food, and instead invites another conclusion, such as that Parisians hate cooking for themselves and never eat at home. This form of counterevidence lurks in the factoid in option A that there are also more Lebanese restaurants in Paris than in any other European capital. However, an especially large number of Lebanese restaurants isn't tremendously significant in itself; the anti-author would have a much stronger counterargument if, for example, Paris had more Chinese, Japanese, Thai, Indian, Mexican, Brazilian, North African, Central African, etc., restaurants than any other European capital, too. Option A provides evidence against the author's contention, but it's not strong evidence.
B. French Cordon Bleu cuisine is very expensive
The fact that U.S.-style fast food is cheaper than expensive French food (option B) might provide the basis for a plausible explanation of why there are a large number of burger & fries joints in Paris. The counterargument here would be that Parisians don't really like burgers and fries; they're just too poor to visit Cordon Bleu restaurants every night. But for this argument to hold much weight, you'd have to assert (and demonstrate) either that burger & fries joints are the only realistic low-cost alternative to Cordon Bleu restaurants for consumers, or that (as in option A) Paris has a huge number of cheap restaurants of all types—pho shops, falafel stands, noodle shops, taco trucks, etc.—and that burger & fries joints are numerous only in the same sense that these other low-cost places are. But option B fails to make either assertion.
C. The number of French tourists eating in New York burger restaurants is very low
Another type of counterevidence would be to see what the eating habits of French tourists are in the United States—the home of junk food. Presumably if French people in the U.S. don't eat at McDonalds very often, it follows that they don't love McDonalds in Paris either. But this is an indirect form of evidence at best. In the first place, French tourists don't represent the general population of Paris. For one thing, they are probably more affluent on average than members of the home population; and for another, they may be less inclined to buy fast food during a vacation than they might be at the end of a long workday—indeed, they may be much more careful than usual about not wasting their limited number of meal opportunities in the U.S. eating junk food that they can get at home. The argument that option C provides some counterevidence to the author's contention is undoubtedly true, but I don't see it as being any more damaging to the author's contention than option A is.
D. Junk food is actually has high nutritional value when eaten in moderation
Option D contradicts the assertion that French people love junk food only if we accept the further argument that French people frequent hamburger & fries joints not because they love the food but because the food is so nutritious. This is a silly argument.
E. There are an unusually large number of American tourists in Paris who eat at burger joints.
The final argument offered is that all those burger & fries joints in Paris are there primarily to serve not the citizens of Paris but the tourists from Omaha (Nebraska, not Beach). In effect, the argument here is that Parisians don't love fast food; they just sell it to U.S. tourists. The stipulated fact that an unusually large number of U.S. tourists in Paris eat at U.S.-style burger & fries joints there provides a direct explanation for why there might be so many such joints in Paris. And because the number of U.S.-style fast-food restaurants in Paris is the central piece of evidence backing the author's contention that French people love junk food, counterevidence that those restaurants serve a large number of non-Parisians directly weakens the author's argument—and does so more forcefully than any of the other options do.
The above analysis leads me to the conclusion that option E "if true, would most weaken the author’s contention"—which is the issue to be decided here. In fact, I would arrange the options in order from "most weaken" to "least weaken" as follows: E, A, C, B, D. But characterizing this practice question as a measure of "Reading Comprehension" is somewhat misleading. It has virtually nothing to do with understanding the meaning of the block paragraph that opens the question; instead, it is almost entirely devoted to analyzing the relevance of five statements offered as logical counterweights to the factual detail that the author of the block paragraph presents as evidence for his (or her) core contention. The connection of this exercise to English language and usage is, I think, extremely tenuous.