The pan-European STOXX 600 rose 0.3%, capping another volatile week which started with a bout of bargain hunting in beaten-down sectors that helped the benchmark record a 2% weekly gain.
European bourses started the day with losses of more than 1% after Trump said that he and his wife Melania had tested positive for the coronavirus and were going into quarantine, adding to uncertainty around the Nov. 3 election.
"The market has been volatile of late and valuations are high so this sell-off does not seem to be anything beyond ordinary," said Louise Dudley, global equities portfolio manager at Federated Hermes. "A lot depends on how the virus affects Trump."
Helping markets stabilise into the close were hopes of more U.S. stimulus after data showed job growth slowed more than expected in September in the world's largest economy.
Meanwhile, euro zone inflation fell deeper into negative territory last month, raising pressure on the European Central Bank to add stimulus.
A second wave of coronavirus cases in Europe has kept investors on edge, with Paris set to be placed on maximum COVID-19 alert from as soon as Monday, a move likely to force the closure of restaurants and bars and impose further restrictions on public life.
Euro zone stocks slipped, while UK's FTSE 100 rose 0.4% at the end of a big week for Brexit negotiations.
German Chancellor Angela Merkel said she had no breakthrough to announce in European Union talks with Britain but remained optimistic that sealing a new trade deal was still possible before the end of the year.
Among individual stocks, Spanish engineering and infrastructure group ACS surged 25.8% after French rival Vinci made an offer to buy ACS's industrial unit Cobra for 5.2 billion euros (4.7 billion pounds).
Vinci rose 4.4%, driving Europe's construction & materials index up 1.7%.
French telecom companies Orange, Bouygues and Iliad rose between 1.1% and 2.6% after the results of an auction of the country's 5G spectrum sale.
Gold miner Centamin slumped 22.2% to the bottom of the STOXX 600 after it forecast a fall in annual production as it delayed some open-pit mining operations at its key Sukari mine in Egypt.
By Sruthi Shankar