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* STOXX 600 set to end flat for the week

* Sanofi tumbles on dour forecast

* NatWest sinks on FCA probe, outlook downgrade

* Energy stocks limit losses

Oct 27 (Reuters) - European shares were muted on Friday, with France's blue-chip index lagging peers following a dour forecast from Sanofi, while gains in energy shares on higher crude prices helped keep declines in check.

The pan-European STOXX 600 was steady at 433.37 points by 0839 GMT, with healthcare shares the top losers, down 1.4%.

Shares of Sanofi sank 15.7% to the bottom of the STOXX 600 as the French drugmaker flagged lower profitability for shareholders next year.

The move pulled France's CAC 40 index 0.6% lower.

NatWest shed 10.3% on a profit outlook downgrade amid Britain's Financial Conduct Authority (FCA) probing the lender's handling of a decision to close former Brexit Party leader Nigel Farage's accounts.

"From a reputational standpoint this is hugely damaging," said Michael Hewson, Chief Market Analyst at CMC Markets UK.

"Even accounting for the increased competition for customer deposits the revelations of unprofessionalism this week about some of its staff could prompt some customers to take their business elsewhere."

Adding to the pressure on the STOXX 600 was a 11.4% drop in Electrolux after the Swedish home appliances maker missed quarterly profit estimates, while spirits maker Remy Cointreau slumped 9.9% on an annual forecast cut.

Media stocks were also among top sectoral decliners, with Universal Music Group down 5.9% after third-quarter results.

Cushioning the benchmark index, energy stocks climbed 1.5% as oil prices rose by over $1 on concerns over a potential widening of the Israel-Hamas conflict.

Britain's commodity-heavy FTSE 100 rose 0.3%, while equities in Spain, Germany and Italy rose between 0.4% and 0.7%.

A pullback in U.S. Treasury yields following signs of easing inflationary pressures on Thursday offered relief ahead of the crucial personal consumption expenditure (PCE) reading later in the day.

The European Central Bank's decision to pause its interest rate hikes on Thursday also lifted sentiment, helping equities weather losses driven by downbeat earnings reports.

The STOXX 600 is set to send roughly unchanged for the week.

Among other stocks, Ubisoft jumped 9.6% to the top of the STOXX 600, as the video game maker's second-quarter bookings surpassed estimates.

Signify rose 9%, boosted by upbeat quarterly core earnings. (Reporting by Amruta Khandekar; Editing by Varun H K)