* Dollar index languishes near one-month low
* Non-farm payrolls on Thursday key to dollar outlook
* RBA and ECB policy meetings also in focus this week
* Some market talk that BNP fine may weigh on euro
LONDON, June 30 (Reuters) - The euro traded flat against the dollar in early European Monday trade, with investors' eyes on a first estimate of euro zone inflation for June ahead of the European Central Bank's monthly meeting on Thursday.
No action is expected from the ECB this week but the euro has been creeping higher since mid-June, retaking some of the ground lost after the bank took steps to pump yet more money into the economy a month ago.
All of the broader market and economic trends that have supported the single currency this year remain intact but many analysts are again pointing towards growing momentum in the U.S. economy, despite disappointing growth numbers last week.
There is also talk amongst dealers of the impact of a large fine expected on BNP Paribas from U.S. authorities that could force the French bank to exchange billions of euros for dollars.
"There is a debate going on about the extent to which they have hedged this deal," said a London-based strategist with one large European bank.
"They may well have a lot of it already. They do have a U.S. business, but it does look like a lot of money that might have at least a temporary impact on the euro."
Sources familiar with the matter told Reuters over the weekend that U.S. Justice Department was expected to announce a settlement with BNP involving a record fine of nearly $9 billion over alleged U.S. sanctions violations.
Another fine a month ago, on Swiss bank Credit-Suisse, shocked the dollar higher against the franc.
The dollar has been in weak form in recent weeks and was still close to a more than one-month low against a basket of major currencies on Monday. Some backward-looking U.S. data last week gave investors no reason to expect higher U.S. interest rates anytime soon.
This week, all eyes are on non-farm payrolls figures due a day earlier than usual on Thursday, expected to show the creation of another 210,000 jobs in the past month.
"If we get a strong print on Friday, it will be the fifth time in a row that we have been over 200K," said Peter Kinsella, a strategist with Germany's Commerzbank in London.
"It should only be a matter of time before the dollar finally begins to gain some traction. The euro will probably trade in a very tight range but it is probably a sell on the rallies."
The euro was 0.05 percent stronger against the dollar at $1.3675 in morning trade in Europe.
Annual inflation in Germany, harmonised to compare with other European Union countries, accelerated to 1.0 percent from 0.5 percent in May. Analysts have forecast euro zone inflation steady at 0.5 percent.
The dollar index was last at 80.019, a touch lower on the day and not far from levels of 80.014 touched on Friday and not seen since May 21. Last week's fall was its biggest in more than two months, and put it on track for a flat half-year.
The dollar drifted down 0.1 percent to 101.37 yen, having hit a 5-week low of 101.235 yen earlier.
"Most people said the U.S. dollar should be stronger than the yen in the first half of the year based on higher Treasury yields," said Masashi Murata, currency strategist at Brown Brothers Harriman in Tokyo.
"Some people might try to sell the dollar/yen more (from here)." (Editing by Andrew Heavens)