* STOXX 600 up 0.1 percent at close
* L'Oreal rallies on ownership change talk
* DAX stays near 2-month high before national election (Adds detail, updates prices at close)
LONDON/MILAN, Sept 22 (Reuters) - European shares steadied on Friday, as tensions over North Korea kept some investors on the sidelines ahead of a national election in Germany that conservative Chancellor Angela Merkel looks set to win.
French cosmetics giant L'Oreal was a notable gainer on speculation about ownership changes, rising as much as 6.7 percent after billionaire Liliane Bettencourt, whose family founded the firm and still owns the largest stake in it, died.
Traders said her death could fuel talk of Nestle selling its stake in L'Oreal, which in turn might look at selling its holding in Sanofi. Sanofi edged up 0.3 percent while Nestle reversed earlier gains to end 0.2 percent lower.
The pan-European STOXX 600 index closed 0.1 percent higher. Britain's FTSE 100 outperformed with a 0.6 percent gain, buoyed by a fall in sterling following a closely-watched speech on Brexit by Prime Minister Theresa May.
Miners were among the biggest sectoral fallers, down 0.2 percent, as saber-rattling over the Korean peninsula and a rating downgrade on China hit metal prices.
North Korea said on Friday it might test a hydrogen bomb over the Pacific Ocean after U.S. President Donald Trump threatened to destroy the reclusive country.
"The North Korean impact isnt always a major sell-off, sometimes its a lack (of) bullish sentiment," David Madden, market analyst at CMC Markets UK, said.
Germany's blue chip DAX index was little changed, holding close to a two-month high on the last trading day before voters in Europe's biggest economy go to the polls.
The DAX has outperformed euro zone peers over the past four years to hit a record high in June. There are expectations that a Merkel victory -- which appears almost certain -- could further support the country's equities, regardless of the make-up of her coalition.
But some German stocks, especially industrials like carmakers, may be too highly valued and could be hit by any correction in key export market China on the back of a growing pile of debt.
"The risks in a lot of the German companies are being under-appreciated," Luiz Sauerbronn, who helps manage $30 billion at global investment advisory firm Brandes Investment Partners, said.
He said he was more optimistic about European equities as a whole given attractive relative valuations versus the U.S., and saw opportunities in British grocers or European oil companies.
Among German blue chips, Deutsche Boerse dropped more than 4 percent after the country's financial regulator took a critical view of a settlement between the exchange and Frankfurt prosecutors in an insider trading case.
Among other top movers on Friday, British engineer Smiths Group Plc fell 6 percent after full-year revenue growth fell short of analyst expectations.
(Reporting by Danilo Masoni and Kit Rees; editing by John Stonestreet)