USA is the leading country of the free world (by having the heaviest cultural, economic and technological impact), so by transitive property Joe Biden, being the leader of that country, is also the leader of the free world.
I don't believe Trump is the leader of the free world. But I do believe, "Trump is the leader of the free world", while completely false and wildly inaccurate, is closer to the truth than "Joe Biden is the leader of the free world".
I don't particularly believe that people in the US, or internationally, want a free world. I think for the most part they want to be free to tell me what do to. Which is not going to happen.
But no, Trump is not, currently, President.