Zeitouni, 25, was killed by two French nationals, Claude Khayat and Eric Robic, who fled back to France to avoid standing trial in Israel.
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France has so far refused to extradite the two, saying French citizens should be tried in France.
Paris urged the Zeitouni family to file a complaint in France, which they did in early July.
“This is a very positive decision, which France welcomes with great relief, because it is the only way to avoid a denial of justice” Bernard Valero, spokesperson for the French Ministry of Foreign Affairs said in a statement.
"This action will at last allow justice to take its course."
Paris authorities said the police have launched a manslaughter probe, which will also look into allegations that the two hit Zeitouni and left her for dead.
A statement by the family said that "After preparing the legal ground in France and speaking with French government officials, we have decided to take their advice and let Paris authorities deal with the case.
"We were assured by the head of the Jewish community in France, the French ambassador in Israel and the French foreign minister that all legal measures will be exhausted with those two and the justice will be done.
"We trust, hope and demand that all the relevant bodies in France keep their word and prove that France is a country of law and order – and not a safe haven for fugitives," the statement concluded.
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