The petition, launched on the CitizenGo website four days ago, "opposes the removal of the cross from a public space and emphasises the Christian roots of Europe".
It is addressed to the European Parliament, the centre-right European People's Party and the European Court of Human Rights.
Controversy erupted last week when France's top administrative court gave the town of Ploermel six months to remove the cross above a papal statue in a public square in a bid to comply with laws enforcing the secular nature of public spaces.
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Although the statue of the late pontiff itself is not in question, the court's move drew ire in heavily Roman Catholic Poland where the Polish-born saint is widely revered and religious symbols are not restricted by law.
Rightwing Prime Minister Beata Szydlo offered last weekend to move the statue to Poland to "save it from censorship", calling John Paul II "a great European" symbolising a "united Christian Europe".
Szydlo added that "the dictate of the political correctness -- the secularisation of the state -- opens the door to values that are culturally alien to us and that lead to Europeans being terrorised in their daily lives".
Gifted to Ploermel by the Georgian-born Russian artist Zourab Tseretel, the statue which features a cross on the arch framing it, was installed in a public square in October 2006.
A local citizens group then launched a legal drive to remove the cross citing a century-old French law on the separation of church and state, but the town's mayor refused.
After years of legal wrangling, France's top administrative court ruled last Wednesday that the cross must go in line with the 1905 law that rules out "raising or affixing any religious sign or emblem" in a "public place".
The court's decision also drew protests from representatives of the Roman Catholic church in France while conservative French lawmaker Nadine Morano said Wednesday she was launching a separate petition "to include the Christian roots of France in the constitution".
In a twist, Budapest on Thursday also offered to take the statue and cover all transport costs.
The foreign ministry said its French envoy contacted authorities in Brittany but had not yet received a response.
"From the point of view of Europe's future, any decision that aims at restricting Christianity and the removal of Christian symbols by referring in a hypocritical way to tolerance is incredibly damaging," Foreign Minister Peter Szijjarto told the MTI state news agency.
Like his Polish ally, Hungary's populist Prime Minister Viktor Orban has positioned himself as a vocal defender of European "Christian identity", which he says is under threat from Muslim refugees.
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