Anything Noam Chomsky, who is not a historian nor has ever had any academic training in the history of Vietnam or the Vietnam War, says is essentially bullshit. However, let's look at the argument and see if we can't find some truth in it all.

That with the Geneva Accords (1954), the French agreed to leave and both the North and the South were planning for unity through a political resolution and that the communists (who were mainly just nationalists) had overwhelming support. And thus would have won any fair elections.

Now, this isn't entirely bad. The French did indeed agree to leave after the Geneve Accords which settled the French Indochina War. There were going to be elections regarding whether or not the two Vietnams were going to unify. So far, so good. However, Chomsky's portrayal of the North Vietnamese government as nationalists is completely false. Not even orthodox historians on the Vietnam War agree to this characterization of the Viet Minh and the post-war government. To create a broad front and unite different dissenting groups is part of the overall Maoist strategy of waging a successful guerrilla war. However, the North Vietnamese government was communist through and through - but they were also fighting for the independence of their nation.

That the U.S. violated this agreement, supported an unelected and unrepresentative government that it called South Vietnam, where in reality most South Vietnamese didn't support it.

It wouldn't be correct to say that the US violated this agreement when in reality, it was the then South Vietnamese government who did. They most certainly did support and unselected and unrepresentative government - but South Vietnam was not a creation of the United States. There were definitely minority groups who were wholly against the South Vietnamese government and Diem certainly made some choices which created ire amongst the rural population (like the extension of conscription), but at best, there was a feeling of indifference towards the government. For many South Vietnamese peasants, their country essentially ended at the borders of their hamlet and many looked with suspicion at both government officials as well as simply individuals from other villages.

That the war was mostly the U.S. bombing the hell out of South Vietnam villages while claiming it was there to save South Vietnam from the North Vietnam communists and "pacify" "rebel" "aggression" in the South.

As a military historian, this was always what annoyed me with Chomsky. This is not what characterized the war in South Vietnam. The US made plenty of mistakes in the Vietnam War, like treating a counterinsurgency conflict like it was a conventional conflict and sending ill-trained conscripts and volunteers to fight a war which they were simply not equipped to fight. However, the way Chomsky paints it out is deliberate killing of civilians and as a sort of 'imperialist genocide'. The US was there to protect South Vietnam. That is something that shouldn't be forgotten. These were insurgents who were supported by the North to overthrow the South Vietnamese government and insert communist rule under the unification with the North. What also bothers me is that Chomsky completely throws out the actual perspective of the ordinary South Vietnamese civilian or even soldier.

I've written countless of posts on this topic, so I'll be happy to link to some here which might be of interest:

To what extent was counterinsurgency actually successful in Vietnam?

How much truth is there to the popular depictions of U.S. Vietnam war combatants and operations?

Did most people in South Vietnam want to unify with North Vietnam under communism?

That while the Paris Peace Accord (1973) to end the war agreed to a political unification (similar to the initial agreement that the U.S. ignored), Nixon and Kissinger deliberately misreported the agreement (and the press followed along) as establishing a separate South Vietnam, allowing them to blame the North as breaking the agreement.

This is referring to Chapter V, Article 15 of the Paris Peace Accords:

The reunification of Viet-Nam shall be carried out step by step through peaceful means on the basis of discussions and agreements between North and South Viet-Nam, without coercion or annexation by either party, and without foreign interference. The time for reunification will be agreed upon by North and South Viet-Nam-

Pending reunification:

(a) The military demarcation line between the two zones at the 17th parallel is only provisional and not a political or territorial boundary, as provided for in paragraph 6 of the Final Declaration of the 1954 Geneva Conference.

(b) North and South Viet-Nam shall respect the Demilitarized Zone on either side of the Provisional Military Demarcation Line.

(c) North and South Viet-Nam shall promptly start negotiations with a view to reestablishing-normal relations in various fields. Among the questions to be negotiated are the modalities of civilian movement across the Provisional Military Demarcation Line,

(d) North and South Viet-Nam shall not join any military alliance or military bloc and shall not allow foreign powers to maintain military bases, troops; military advisers, and military personnel on their respective territories, as stipulated in the 1954 Geneva Agreements on Viet-Nam.

South Vietnam can definitely not be blamed for not following through on this because within two years, Saigon had already fallen. Throughout 1973 and 1974, the People's Army of Vietnam constantly broke the ceasefire (and thus, the accords) by military raids into South Vietnamese territory, culminating in the 1974 Ho Chi Minh campaign.

I actually agree with much of Chomsky's interpretation. He may be wrong on some points as he is not a historian, but he is right on the broad outlines. He was one of the most prominent anti-war intellectuals at the time, so he knows a bit about it, and also his bias is pretty obvious. I do think it's fair to say that his views are somewhat naive, maybe intentionally so. He seems to have an idealistic view of human nature, and he also seems to subtract the moral element of political values from his analysis. For Chomsky, it doesn't matter whether the Vietnamese were ruled by a communist or non-communist state. This might strike some as wrong, but I am sympathetic to the idea that taking this kind of view can cut through propaganda and focus on the means rather than the ends. Then it is impossible not to conclude that the American war in Vietnam was truly shameful.

To get to your main points, the United States did disregard the Geneva Accords, and propped up a dictatorship in South Vietnam. The Viet Cong were not "mainly nationalists", they were Marxist-Leninist and Maoist. Sure, they were essentially waging a war of national independence for a united Vietnam - but of course, under the Communist Party. The South Vietnamese government was initially led by a man named Diem, who came to power in a referendum marked by electoral fraud. Diem was a nationalist and a Catholic who repressed the Buddhist majority. The "Buddhist crisis" was resolved with a military coup against Diem, who was assassinated. The Pentagon Papers suggest that the US was very worried about the Buddhist crisis, aware of the coup, and wanted Diem gone. To say that this was a government with popular support and legitimacy seems incorrect. Not everyone supported the Viet Cong, and they were not "good guys", but it was an indigenous insurgency against an authoritarian regime.

If the US supporting the South Vietnamese government does not constitute an invasion of Vietnam, then the Soviet Union supporting the Communist government in Afghanistan was not an invasion of Afghanistan. My belief is that both were invasions. In both cases, the government controlled urban areas, principally Saigon and Kabul respectively. The rural areas were areas where the Viet Cong and the Mujahideen could operate among the population. In Vietnam, the American war devastated the countryside. This resulted in a migration of millions of people previously part of the rural population to the cities.

Samuel Huntington, writing in Foreign Affairs in 1968, says,

The principal reason for this massive influx of population into the urban areas is, of course, the intensification of the war following the commitment of American combat troops in 1965. About 1,500,000 of the total increase in urban population is accounted for by refugees, half still in refugee camps and others settled in new areas. At least an equal number of people have moved into the cities without passing through refugee camps...

After the war, massive government programs will be required either to resettle migrants in rural areas or to rebuild the cities and promote peacetime urban employment. In the meantime, while the war continues, urbanization is significantly altering the balance of power between the Saigon Government and the Viet Cong.

More than anything else urbanization has been responsible for the striking increase in the proportion of the population living under Government control between 1964 and 1968. The depopulation of the countryside struck directly at the strength and potential appeal of the Viet Cong. For ten years the Viet Cong had waged a rural revolution against the Central Government, with the good Maoist expectation that by winning the support of the rural population it could eventually isolate and overwhelm the cities.

...if the direct application of mechanical and conventional power takes place on such a massive scale as to produce a massive migration from countryside to city, the basic assumptions underlying the Maoist doctrine of revolutionary war no longer operate. The Maoist-inspired rural revolution is undercut by the American-sponsored urban revolution.

As a side note, how on Earth did our relationship with Vietnam recover to what it is today?

This is of course a complicated topic, but Vietnam began market reforms in the mid 1980s, and like China before it found it useful to normalize relations with the United States. Key to this effort was none other than Senators John McCain and John Kerry, among other veterans who are somewhat less famous now, who have received a great deal of very deserved credit for pushing US foreign policy towards burying the hatchet, so to speak. Relations were more or less normalized in 1995, although as that pushes against the twenty year rule I would advise going to /r/AskSocialScience for more.