In his annual State of the Union speech at the European Parliament, Juncker said he would seek to initiate free trade talks with Australia and New Zealand.
"Today, we are asking that we open up negotiations with Australia and with New Zealand," he said.
"I am asking that we complete these negotiations by the end of our mandate (in late 2019)."
He also said he would seek powers to screen foreign takeovers in Europe's strategic sectors, amid worry about investment by China.
"We are not naive free traders. Europe will defend its strategic interests with an EU framework for investment screening.
He said "the wind is back in Europe's sails", as the continent becomes more united and economic momentum picks up a year after Brexit.
"We have now a window of opportunity but it will not stay open forever. Let us make the most of the momentum, catch the wind in our sails."
Juncker recalled that when he gave the same speech last year that the European Union was "not in a good state."
It was a year when the 28-nation bloc was "shaken to our very foundations," he said, following the British vote to leave, the rise of populism, the migration crisis and economic troubles.
"We only had two choices, either come together around the positive European agenda or each retreat into our own corner," the former Luxembourg premier said.
"Faced with this choice I argued for unity," he said, "I proposed a positive agenda to create a Europe that protects, a Europe that empowers, a Europe that defends."
European finance minister
Juncker also proposed the EU create its own Europe-wide finance minister, a big step towards deeper integration of the eurozone.
The proposal matches a similar demand by French President Emmanuel Macron, who believes that the eurozone needs stronger institutions in order to avoid shocks such as the debt crisis or Brexit.
"We need a European Minister of Economy and Finance," Juncker said.
"I am not calling for a new position just for the sake of it. I am calling for efficiency," Juncker said.
Appeal for press freedom
Juncker called on Turkey to "let our journalists go" following its arrests of French and German journalists under a broad human rights crackdown.
"I appeal to the powers that be in Turkey, let our journalists go!," Juncker said in his annual state of the union speech.
