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All four of their previous continental finals had finished 0-0, with them winning on penalties in 1992 and 2015, both times against Ghana, and losing the other two.
Zaire-Emery became the youngest ever French goalscorer in the Champions League at 17 years and 280 days.
City started their title defence by coming from behind to beat Red Star Belgrade 3-1 at home.
City's striker and Spain's World Cup winner won the prizes at a ceremony in Monaco.
England captain Kane, who joined for a league record 100 million euros last week to solve Bayern's scoring problems, slotted their second goal in the 74th minute after setting up Leroy Sane for a fourth-minute opener.
Bayern did not disclose the transfer fee, which media reports have put at around 100 million euros ($109 million). That would be a Bundesliga record.
Medical examinations showed the 30-year-old right-back has lymphoma and he will now have several months of treatment.
The 32-year-old has a contract until June 2025 with an option for a further year, while the Spanish champions also said they had included a buyout clause of 400 million euros ($435.72 million).
Gundogan will leave City after captaining the English club to the Premier League, FA Cup and Champions League last season, ending a successful seven-year stint in England where he won 14 trophies, including five league titles.
The player would be free to negotiate and sign a pre-contract agreement with a new club from January should he decide to see out the remaining year of his deal at PSG.