* Euro struggles after ECB's surprise cut, French downgrade
* Traders cautious about dollar before U.S. jobs data
* In-line reading could see dollar give up recent gains
LONDON, Nov 8 (Reuters) - The euro fell for a second day on Friday, hurt by the European Central Bank's surprise interest rate cut and a downgrade to France's credit rating, while the dollar inched up before a key U.S. jobs report.
A strong non-farm payrolls report would increase expectations the Federal Reserve will start tapering its bond buying programme sooner rather than later, particularly after Thursday's robust U.S. growth figures. But many are cautious about buying the dollar given the risk of a soft jobs reading due to last month's 16-day government shutdown.
That could see the dollar index give up some of its gains, having hit a near two-month high of 81.46 on Thursday. A dip in the dollar would also offer a reprieve to the euro which is on track for its second week of losses.
"An in-line reading for the U.S. jobs number will see the dollar come off," said Neil Mellor, currency strategist at BNY Mellon. "A better-than-expected number will give the dollar a boost, but recent commentary from the Fed suggests that they are not in a hurry to withdraw stimulus."
Economists polled by Reuters estimate the unemployment rate rose to 7.3 percent in October while non-farm payrolls grew by 125,000 jobs. The payroll figure is likely to show some impact from the partial government shutdown.
Against the dollar, the euro was down 0.1 percent at $1.3408 , having hit a seven-week low of $1.3295 on Thursday. The euro was also hit in Asian trade after Standard & Poor's downgraded France's credit rating to AA from AA+.
The euro had fallen sharply on Thursday after the ECB cut borrowing costs to a record low of 0.25 percent and said it could reduce further to prevent the euro zone's recovery from stalling following a sharp drop in inflation.
"Given the ECB's view of a prolonged period of low inflation, any further slowing in CPI will raise the threat of negative deposit rates - which will be a big negative for the euro," said Chris Turner, chief currency strategist at ING.
"And even the taboo subject of QE from the ECB could be brought into discussions."
Indeed, money markets and the currency options market are showing signs that the euro will grind lower in the near term as it loses its yield advantage over other major currencies.