Short answer: Most dominant power in Europe? No. But if by "Dominant power in Europe" you mean "Most militarily powerful Western European country", then maybe, however both the USSR and the USA were significantly more important in Europe than France was.
Longer answer: In the 1960s France, under President de Gaulle, largely broke with its WW2 allies and attempted to reassert its 19th and early 20th century place as an independent world power. This reorientation should be contextualised within France's military humiliations in the post WW2 world, notably in Vietnam and in the Suez Crisis. These failures led to France's (and in the Suez Crisis, the UK's as well) realisation that they could no longer operate as independent world powers. The UK reacted to this by becoming more closely aligned with the US, relying on their "special relationship" to give the UK some significant say in US foreign policy through their influence in Washington. President de Gaulle, when he came to power in 1958, felt that this special relationship meant that France was a second class citizen in NATO; de Gaulle sent a memorandum to President Eisenhower and Prime Minister Macmillan in 1958 proposing changes to NATO which de Gaulle felt were necessary to rectify this. They were never implemented.
Eventually de Gaulle became convinced that France's future in NATO was always one of subservience, and that to regain a position of influence France needed to leave the US dominated alliance and instead build a European based alliance with France and West Germany forming its core (although France didn't technically leave NATO, they did disengage with its command structure meaning an effective withdrawal). de Gaulle reinvested in France's military and instituted an independent nuclear weapons program, ensuring that France would not have to rely on the US' nuclear arsenal to deter the USSR from invading Western Europe. However, despite normalising relations between France and West Germany, de Gaulle was largely unsuccessful in building a European alliance as a counterweight to US dominance in Europe, as West Germany, particularly under Chancellor Adenauer, remained a staunch US ally. de Gaulle's insistence on good French-German relations did however help to form the foundations of the modern EU.
TL;DR In the 1960s France under de Gaulle attempted to regain its position as a world power. Despite significantly increasing France's military might, de Gaulle was unable to create a third pole in the bipolar Cold War world; both the USSR and the USA remained more diplomatically and militarily important than France, even in Western Europe.
Much of this info has come from Kissinger's Diplomacy which, while far from the least biased source, was written by someone intellectually active in geopolitics in the relevant time period.
Because ManicMarine has been talking about military, i'll talk about the other aspects. It is clear that during the 60-70s era, the France's army was probably the strongest on the continent - yet not even closely rivalling the US or the USSR. Like it's been said, nuclear deterrence was at the center of De Gaulle's foreign policy strategy and helped France gain more independence vis a vis NATO.
Amongst European nations, France's economy was doing much better than its British, Italian and Spanish neighbours during that period of time. And Germany was fragmented.
It is important to note the importance of the "Trente glorieuses" (45-75 era) as the period of French economic success, which were ended by the 70s oil shocks (French budget hasn't been balanced since then - yes, every single year for the past 40 years :D)
With the fragmentation of Germany and the deindustrialization of the UK, France and its robust corporations in different industries, its world-renowned engineers, its significant population and its strong interior market (wages have been relatively high since Front Populaire) was able to create a very dynamic and growing economy. The birth of globalization and the rise of oil prices ended this dynamic, and the French have been experiencing relatively high unemployment and low growth rates since then.
So to the question "Was France the dominant power in Europe" at that time, probably not. It could not exerce the influence that the US exerted on most western countries. But it was a regional leader that somehow balanced and relativized US influence in Western Europe. It was the most powerful European country in terms of culture, military and economy for that short period of time - yet was not outclassing its peers at all (I mean England, Germany, Italy?).
It's also important to note that however badly it ended, France still had a significant colonial empire in the early 60s!