France's services sector activity shrank steadily in October on weak demand, a business survey showed on Monday, highlighting the headwinds facing the euro zone's second-biggest economy.

The HCOB France final purchasing managers index (PMI) for the services sector, compiled by S&P Global, stood at 45.2 points in October.

That was up from 44.4 in September but still well below the 50 mark dividing growth in activity from contraction.

It was also below the flash PMI services number for October which came in at 46.1 points.

The final October composite PMI figure - which combines both the services and manufacturing sectors - stood at 44.6 points. This was up from 44.1 in September but also below a flash October composite PMI which had stood at 45.3 points.

"The French services sector is taking a heavy blow from sluggish demand. Both overall and external new orders are plummeting rapidly, resulting in a strong decrease in business activity," said Hamburg Commercial Bank economist Norman Liebke. (Reporting by Sudip Kar-Gupta; Editing by Hugh Lawson)