An old war hero, seizing power in a quasi coup d'etat and then asking for untethered power. It sounds very similar to the rises to power of both Marshal Petain and also Napolean. Therefore my question really is, why is he such a hero in France? Were the French people not nervous that he'd become a dictator like those before him? Why was there so much trust in him, a man who was hated by the Americans and disliked by Churchill?
De Gaulle was more than just a "war hero"; he was effectively the leader of the Free French Forces, and therefore the face most people put on the French resistance against Nazi rule during and after the war. Pétain was a fairly popular military figure before WWII, and his fall from grace resulted from his association with national treason more so than with political authoritarianism. De Gaulle was a symbol of patriotism and (if need be strong-handed) national unity, much like the equally celebrated Napoléon; Pétain sure as hell was not.
He also oversaw an era of economic prosperity and modernization similar to that of the US or Germany at the time and which is known in France as the Trente Glorieuses. It was associated with rapid post-war recovery, the welfare state, economic stability, high living standards, full employment, job security, rising wages, meritocracy, etc. This status quo started breaking down in the '70s, after De Gaulle left power.
Moreover, De Gaulle's devout — and at times shadowy — political entourage (people like Foccart or Debizet) deliberately took on the burden of handling the most unsavory aspects of his presidency in an effort to ensure his image remained untarnished. Self-serving neo-colonialist meddling (Françafrique), the existence of a quasi-secret police (Service d'Action Civique) or the forced disappearance of a high-profile anti-imperialist activist (Ben Barka affair) are usually not associated with De Gaulle personally by the general public because he technically wasn't directly involved with those. His close supporters knew he was a charismatic figure and wanted it to remain that way — effectively a calculated cult of personality. In post-war France, De Gaulle emerged as more than a general or politician — he was a myth, and remains so to this day.
I should add that even in France De Gaulle didn't enjoy unquestioned, uninterrupted popularity throughout his presidencies. During the Algerian war and subsequent crisis (which precisely saw his return to power and the institution of a stronger executive through what was effectively coup), he was disliked by many French settlers in Algeria and the hardline opponents of Algerian independence. He drew particular ire from the terrorist Organisation Armée Secrète who made a failed attempt on his life in 1962. Some on the far-right fringe still resent De Gaulle as a traitor because of his Algerian policy.
And of course there was May 68. De Gaulle was singled out by left-wing protesters as the embodiment of everything they hated: Bureaucratic capitalism, French nationalism and imperialism, paternalistic-moralistic conservatism, control of information, police brutality and union busting, etc i.e. the right-wing establishment they sought to bring down. That's when he started becoming a lot more divisive as a political figure, and he stepped down not long after that following a referendum that didn't take the direction he wanted.
De Gaulle's unpopularity among a segment of US policymakers on the other hand was first and foremost related to his critical stance towards (US-dominated) NATO and his promotion of a sovereign military and foreign policy. Many in post-WWII France saw the US with suspicion precisely because they feared their superpower ally might be tempted to get overbearing and compromise that very independence as a result.