Juncker's proposals ensure fair competition in the European Union and also offer better protection against company acquisitions that do not comply with market rules, she said. "The wind is back in Europe's sails, it now has a window of opportunity".
But he says the PM's Brexit negotiators should consider tweaking demands on borders and other key issues to help win over the EU's most influential players.
Juncker said there was a good chance that the European Union would agree the main elements of a new free trade with the Mercosur countries of Argentina, Brazil, Paraguay and Uruguay and of an updated trade partnership with Mexico by the end of this year.
In a speech setting out the future direction of the bloc, Jean-Claude Juncker said the UK's exit would be a "sad and tragic" moment, but it was "not the be all and end all".
Juncker wants to boost trade deals and finalize pending ones by the end of 2019, saying that countries around the world were "knocking at our door" for new agreements.
"We have said this in the Article 50 letter that deals with both economic co-operation and with security co-operation".
Juncker's speech was full of calls for "more Europe", especially his suggestion that Bulgaria, Romania and Croatia should all finally become full members of the Schengen zone.
"Accession candidates must give the rule of law, justice and fundamental rights utmost priority".
And Defence Secretary Sir Michael Fallon said the UK's role in the continent's defence had "never been more vital".
To much applause from the European Parliament, he called on the Turkish government to stop attacking EU leaders and to "let our journalists go".
European Commission President Jean-Claude Juncker has warned that Britain will regret its decision to leave the European Union and that the bloc will "move on" after London's departure.
He will call for countries that are outside the eurozone and the Schengen passport-free area to join, they added.
The European Union was not a group of "naive free traders" and would always defend its strategic interests.
During his wide-ranging annual speech, Juncker said that the European Union has "regained confidence in the past years".
"We have said we want a strong and prosperous EU".
The opposition Labour Party has already said it plans to vote against the bill unless the government comes forward with concessions, and has said several clauses in the legislation amount to a "power grab" by government.
Mr Corbyn's spokesman said: "Labour has from the time of the referendum last summer said we respect and accept the referendum result". "We will need to be prepared to continue in this manner, and to compromise where necessary".