France's Socialists are seeking a centrist alliance in the second round of parliamentary elections to prevent a crushing victory for the ruling UMP.
Ms Royal is struggling to shore up the weakened left
The right-wing UMP, led by President Nicolas Sarkozy, is heading for an election landslide on 17 June after Sunday's first round.
The UMP is on course to win between 383 and 501 seats in the 577-seat National Assembly, up from 359.
The Socialists' Segolene Royal said France needs to have "counterweights".
Her party faces a tricky period of soul-searching after Mr Sarkozy's triumph in the presidential election and the latest blow to the Socialists' fortunes.
Ms Royal, who lost to Mr Sarkozy in the presidential race, said she wanted to prevent an "excessive concentration" of power in the hands of just one party.
She called for an alliance of the Socialists and the new centrist party led by Francois Bayrou - the Democratic Movement (MoDem).
Nicolas Sarkozy looks set for the big majority he is seeking
"It is necessary in a democracy to breathe, it is necessary in a republic to have counterweights to the government," she said on French TV.
"At this point it is clear that the MoDem should join the candidates of the Socialist Party."
Only one of the 110 MPs elected in the first round of voting was a Socialist. The Socialists currently have 149 seats in the assembly.
Mr Bayrou's MoDem party could win some key constituencies, notably Bordeaux, where the mayor Alain Juppe is vulnerable.
Last month Mr Sarkozy recalled Mr Juppe to the cabinet as environment minister, after serving a year-long ban from public office for his role in a party funding scandal.
Analysts say a big majority would allow Mr Sarkozy to press ahead with sweeping economic reforms.
Turnout on Sunday hit a record low, at 60.5%.
That contrasted with a turnout of 84% in the presidential election a month ago.
If candidates do not win more than 50% of the vote, with at least a 25% turnout, the constituency must vote again on 17 June.
Any candidate with a first-round score of 12.5% or more of the registered vote is eligible to stand.
France has not given a single party a second successive parliamentary majority since 1978 - but this time the pattern looks set to change, says the BBC's Emma Jane Kirby in Paris says.
France's "blue wave" means the president will get exactly what he wants - strong backing with which to implement his ambitious programme of economic reforms, our correspondent adds.
The parties of the left - including the communists, who look set for their worst result in memory - have called for a big turnout next week, warning voters not to give absolute power to Mr Sarkozy.
He has said he will hold a special session of parliament in July to initiate his first set of political reforms, which include tougher immigration rules and more freedom for universities.
A new finance bill will mean that overtime earnings are no longer taxed, inheritance tax is abolished for most people and overall individual taxation is capped at 50%.