* Pound firm after UK Labour election win

* U.S. jobs data, French election in focus

* Bitcoin set for biggest weekly win in over a year

* Graphic: World FX rates http://tmsnrt.rs/2egbfVh

* Graphic: Global asset performance http://tmsnrt.rs/2yaDPgn

LONDON, July 5 (Reuters) - Wall Street stocks rose on Friday after data showed U.S. job growth slowed to a still-healthy pace in June.

The Dow Jones Industrial Average gained 0.3%, the S&P 500 rose as much as 0.11% before falling back to trade flat, and the Nasdaq Composite ticked up 0.3%.

Sterling and UK stocks were also higher as Britain's Labour Party won a landslide general election victory after 14 years of Conservative rule.

The market focus in Europe was quickly shifting from the British election - where the outcome of Thursday's vote was widely anticipated - to Sunday's second-round legislative election in France.

French stocks have recovered ground after they were sold off sharply following the surprise election announcement last month. The euro has benefited from renewed U.S. rate-cut speculation.

Trading was steady a day after the U.S. July 4 holiday and following the release of the June U.S. non-farm payrolls report.

U.S. job growth slowed to a still-healthy pace in June, with the unemployment rate rising to 4.1%, increasing the chances that the Federal Reserve will be able to tame inflation without tipping the economy into recession.

"We're in the summer holiday sweet spot for markets, with investors focused on inflation coming down to target in big economies," said Guy Miller, chief market strategist at Zurich Insurance Group.

MSCI's world stock index touched a record high. It remained near there and was last up 0.05%. European shares rallied 0.3%, while Japan's Nikkei and broader Topix also logged record levels.

Following the British election result, London's FTSE 100 index rose 0.38% at the open. The yield on 10-year British government bonds or gilts, dropped 4 basis points to 4.16%, largely in line with other European markets, and sterling inched up to around $1.2797.

"A landslide victory provides the sort of clarity and stability that equity markets need in an increasingly volatile world," said Ben Ritchie, head of developed market equities at Abrdn.

What matters will be revealed more slowly as it becomes clear how Prime Minister Starmer will pay for the faster growth he seeks, said Kevin Gardiner, global investment strategist at Rothschild & Co.

"Even a centrist Labour government will not be as pro-business or libertarian as a Conservative one, and we should anticipate many changes in the detail of tax and sectoral policies in the weeks ahead, some of which will be contentious," said Gardiner.

JOBS IN FOCUS

Non-farm payrolls increased by 206,000 jobs last month, the U.S. Labor Department's Bureau of Labor Statistics said in its closely watched employment report on Friday. Data for May was revised sharply down to show 218,000 jobs added instead of the previously reported 272,000.

Zurich's Miller noted a weakening in recent employment data and said a softer-than-expected payrolls number would support the case for a U.S. rate cut in September.

U.S. Treasury yields were little changed during London trade, with two-year yields trading around 4.64% and benchmark 10-year yields up marginally at 4.32%.

In currency markets, the euro rose to $1.0828 as polls point to France's far-right National Party falling short of an absolute majority at Sunday's parliamentary election runoff.

"If the polls eventually prove accurate, this would mean the more extreme policies of fiscal expansion and immigration curbs are unlikely to pass," said MUFG analyst Michael Wan.

The dollar was down around 160.93 yen. The Australian dollar hovered near a six-month high of $0.6739 as yield spreads swung in its favour, underpinned by wagers that the next move in Aussie rates might be up given inflation is proving stubborn.

Bitcoin was set for its biggest weekly fall in more than a year on worries over the likely dumping of tokens from defunct Japanese exchange Mt. Gox and further selling by leveraged players after the cryptocurrency's strong run.

It slid as much as 8% on the day to $53,523, its lowest since late February.

Gold rose 0.8% to $2,374.80 per ounce and was set for a second straight weekly gain, while oil prices were poised for a fourth straight week of gains.

Front month Brent crude futures were up 9 cents at $87.52 a barrel while U.S. West Texas Intermediate ticked up 11 cents at 83.98.

(Reporting by Dhara Ranasinghe; Additional reporting by Wayne Cole in Sydney; Editing by Edwina Gibbs, Anil D'Silva and Alex Richardson)