Three-way run-offs and horse-trading: what happens next in French elections?

PARIS (Reuters) -Here's how the second round of France's parliamentary election on July 7 will work and the possible scenarios after official results showed Marine Le Pen's far-right National Rally (RN) party had won Sunday's first round.

HOW DOES IT WORK?

Elections for the 577 seats in France's National Assembly are a two-round process.

In constituencies where no candidate won outright in the first round, the top two candidates, as well as any candidate with more than 12.5% of the total number of registered voters in that constituency, move to a second round.

Whoever gets the most votes in the second round wins the seat. 

The high turnout on Sunday means some 300 constituencies are now facing potential three-way run-offs which, in theory, favour the RN. 

To prevent these three-way run-offs and block the RN, France's centre-right and centre-left politicians have long practiced what they call a "republican front", whereby the third-placed candidate drops out of the race and urges voters to rally behind the second-placed candidate.

All candidates through to the run-off have until Tuesday evening to decide whether to stand down or run in the second round.   

HOW IS IT LOOKING THIS TIME?

Many political leaders gave guidance to candidates and voters on Sunday evening. 

President Emmanuel Macron urged a "wide-ranging rally behind republican and democratic" candidates for the second round, effectively guiding against both the far-right National Rally and the hard-left France Unbowed (LFI) party.

His former Prime Minister, Edouard Philippe, explicitly called on the candidates from his party to drop out if they were in third position and rally behind candidates from the centre-left to the centre-right, excluding the RN and LFI.

On the left, the Socialist and LFI leaders also called on their third-placed candidates to drop out to block the RN.

The conservative Republicans party, which split ahead of the vote with a small number of its lawmakers joining forces with the RN, has yet to take a stance.

WHAT WILL HAPPEN NOW?

The effectiveness of the "republican front" has weakened over the years, and many voters no longer heed the advice of party leaders.

It is also possible that candidates will refuse to drop out despite guidance from political HQs in Paris. 

But talks over the next 48 hours will be crucial and could swing the results significantly, potentially deciding whether the RN reaches an outright majority in parliament or not.

That makes the result of the second round extraordinarily hard to predict. Even pollsters have urged caution on their own seat projections. 

(Reporting by Michel Rose; editing by Philippa Fletcher and Alex Richardson)