Investors are on edge over worries that Chinese appetite for big-ticket items could wane as its economy slows, particularly after an Apple warning last week over weaker iPhone sales in the country.

Further clouding the picture is a shift in spending patterns as Chinese consumers, squeezed by a falling yuan, start spending more at home, creating uncertainty for overseas tourist hotspots or shopping destinations.

Switzerland's Richemont, the world's second biggest luxury goods group, said sales growth had slowed in the three months to Dec. 31 in Hong Kong, for instance, the biggest market in the world for watches.

That came on top of problems in France, where a backlash over high living costs led to riots in Paris which according to Richemont "negatively impacted tourism and led to store closures for six consecutive Saturdays".

French companies have this week revealed some 60 million euros (£54.1 million) of lost business from the anti-government demonstrations.

But Richemont -- which also makes Van Cleef & Arpels jewellery, and owns IWC watches and fashion brand Chloe -- signalled sales were still progressing at a healthy pace in mainland China, citing "double digit" growth there.

Chinese shoppers at home and abroad account for over a third of sales in the luxury industry as a whole, and companies are shaking up their approach to corner that clientele, arguing that in the long-term demand will stay strong.

Richemont said in October it was partnering with China's e-commerce giant Alibaba to shore up sales there, and as part of a push to sell more online.

EUROPEAN PAIN

Richemont shares, down over 30 percent since hitting a peak last May when worries over a U.S.-China trade war began to emerge, were up 2.9 percent by 0910 GMT.

Shares in peers including Louis Vuitton owner LVMH, which reports results on Jan. 29, and Gucci parent Kering also rallied.

Overall, Richemont posted a 5 percent rise in sales at constant currencies in the October-December period, its third quarter, excluding recently acquired online distributors Yoox Net-A-Porter (YNAP) and Watchfinder, a second-hand platform.

That marked a slight slowdown from the 8 percent growth in the six months to end-September, though it was in line with consensus estimates cited by analysts.

"Sales grew in all regions, with the exception of the Middle East and Europe," Richemont said. It gave no outlook.

Including YNAP and Watchfinder, Richemont's sales were up 24 percent at constant currencies, in line with expectations.

Analysts at RBC cited Asia as a bright spot - underlying sales there increased 10 percent, down from 14 percent in the prior six month period - and said prospects for jewellery, where Richemont makes the bulk of revenues, were encouraging.

But others like Berenberg pointed to a flat performance its specialist watch brands as a potential headwind for rivals such as Swatch.

(Reporting by Sarah White; Editing by Himani Sarkar and Keith Weir)

By Sarah White