* Far-right's Tanguy may be France's next finance minister

* Tanguy says RN will cut deficit to 3% of GDP by 2027

* Says EU fiscal rule-book must be respected

* Flags plans to encourage business, cut spending

PARIS, June 24 (Reuters) - A new French government led by Marine Le Pen's far-right National Rally (RN) would end the decades-long practice of running high budget deficits and stick to the European Union's fiscal rules, the party's financial pointman told Reuters.

RN lawmaker Jean-Philippe Tanguy is widely seen as one of the most likely candidates to head France's finance ministry if his anti-immigration party wins an absolute majority in the two-round parliamentary election on June 30 and July 7.

"We won't let the deficit run out of control. We won't use any wiggle room, which France no longer has, and we will break with 50 years of systematically running deficits," Tanguy said in an interview conducted on Sunday.

The RN, which Tanguy said had been in contact with unspecified investors in recent days, is keen to demonstrate it can be trusted with the public finances if it takes power for the first time after spending years on the political margins.

President Emmanuel Macron called the snap national election after his centrist party was trounced by the RN in this month's vote for the European Parliament. His move initially triggered a heavy selloff of French stocks and bonds as investors took fright at the prospect of either the far-right or the far-left - both wedded to costly spending policies - taking power.

The RN broadened its support in the EU election far beyond its traditional strongholds in the northern rust-belt and on the Mediterranean coast with promises to reverse the decline in voters' standards of living.

Opinion polls show the RN still ahead of its rivals but possibly falling short of an absolute parliamentary majority.

Tanguy said his party's election programme would be entirely financed by closing tax loopholes, reducing red tape, and spending cuts, especially on welfare for immigrants.

"What I have to say to business people and markets is that the National Rally has no choice but to succeed. We will not have the indulgence (of the financial markets) that Macron enjoyed," he said.

CONCERNS

Investors and ratings agencies have raised concern about RN policies such as a pledge to cut value-added tax on energy from 20% to 5.5%. Standard & Poor's said this could weigh further on France's rating after it downgraded the country last month.

The outgoing government has already had to scramble to find 20 billion euros ($21 billion) worth of spending cuts for 2024 and as much again for 2025 after France's budget deficit unexpectedly widened to 5.5% of national output this year.

Tanguy said France must retain the current government's plan to reduce the deficit to 3% of gross domestic product (GDP) by 2027, in line with its commitments under the European Union's fiscal rulebook, the Stability and Growth Pact.

"The Stability Pact has to be respected," Tanguy said. "France must honour its word."

Financial jitters over French politics have eased slightly in recent days, which Tanguy said could be put down partly to the capacity of the European Central Bank to intervene if necessary to calm markets.

"It has done it before and will do it again independently even if not needed because the French economy is solid," Tanguy said, adding that the vast pool of savings accumulated by the French people could also help to absorb market tensions.

The RN has toned down some of its more radical plans, for example saying that a promise to reduce the retirement age to 60 from 64 for people having worked 40 years would only apply to those who started work before the age of 20.

Jordan Bardella, Le Pen's prime ministerial candidate, also told the French employers' federations on Thursday that an RN government would stick with the outgoing government's plan to cut business taxes.

The strategy appears to be paying off. In an Ipsos survey, published by the Financial Times, the RN is now seen as the most trustworthy party when it comes to managing the economy and public finances.

Tanguy also said an RN government would not scrap Macron's measures to attract banks and funds from London after Brexit.

He welcomed new EU tariffs on imports of Chinese electric vehicles, adding that the RN backed free trade provided it was on fair terms, which he said was not the case with China because of massive state subsidies.

"Maybe China will behave better. In any case, if we can re-establish fair trade that will be good for everyone," he said

($1 = 0.9354 euros) (Reporting by Leigh Thomas; Additional reporting by Elizabeth Pineau Editing by Gareth Jones)