The prime minister met with Mr Trudeau in Madrid on Thursday morning local time, following the NATO Summit.
Speaking on the tarmac before his flight to Paris, Mr Albanese described their one-on-one as "very successful" and an opportunity to work towards their "common view" on tackling climate change and increasing "social inclusion".
"We have very similar political perspectives and Prime Minister Trudeau has invited me to visit Canada. I've invited him to visit Australia," he said.
"We'll wait and see when that happens sometime in the future."
In Paris, Mr Albanese will seek to mend the relationship with the French, after having represented the nation at NATO in Spain.
The prime minister spoke at the "extremely successful" NATO Summit in Madrid on Wednesday, where he warned world leaders of China's assertive and expanding influence in the Pacific, which he said threatened regional security.
"The communique that has arisen from the NATO Summit is one that Australia is strongly supportive of over the last couple of days," he said.
"What we've seen is the world come together in rejecting the Russian aggression on Ukraine, but also having a reassertion of our shared commitment to democratic values of having a rules based international order."
Mr Albanese met with the leaders of Italy, Germany and the European Commission, as well as New Zealand, Japan and South Korea - who alongside Australia form a group known as the Asia-Pacific Four.
He also held a one-on-one with his UK counterpart Boris Johnson, gifting him a Rabbitohs rugby league jersey at their first meeting as leaders, and pledging to work together on security in the Indo-Pacific region and climate change.
Mr Albanese will later on Thursday address the Organisation for Economic Co-operation and Development Council and meet with French business leaders.
The prime minister will on Friday be hosted by French President Emmanuel Macron at the Elysee Palace.
The pair will work on repairing the damaged relationship after the $90 billion submarine deal with Naval Group was dumped.
"That's so important that we reset the relationship," Mr Albanese said.
"France is a power in Europe, but he's also a Pacific power."
It is yet to be confirmed whether Mr Albanese will take up Ukrainian President Volodymyr Zelenskiy's offer to visit him in Kyiv as a show of support for his war-torn country.
The prime minister said security assessments are still underway.
