(CNN) The warning came from across the Atlantic last month.

Richard Burr, the head of the US Senate Intelligence Committee, was presiding over a briefing on the investigation into alleged Russian interference in the US presidential election when he offered his assessment of who the next target might be.

"I think it's safe by everybody's judgment that the Russians are actively involved in the French elections," Burr told reporters. "Part of our responsibility is to educate the rest of the world."

Burr's warning came to fruition this week with the revelation that campaign staff for Emmanuel Macron, the favorite to become France's next president, had been targeted by suspected Russian-linked hackers

The news did not come as a surprise to the Macron camp, or to experts who say Russia may be working behind the scenes to swing the result in favor of his opponent Marine Le Pen.

But while Russia has denied the hacking claims, fears of potential Kremlin interference now loom large over the election as voters prepare to head to the polls for the final round of voting next Sunday.

Why would Russia target France?

Russia says it has no preferred candidate in the French election, but it has good reasons to support Le Pen over Macron.

Le Pen's anti-Europe and anti-NATO stance are perfectly aligned with Russian interests, and she has consistently called for closer ties with President Vladimir Putin.

Le Pen has also expressed a desire to roll back European Union sanctions levied on Russia in the aftermath of the annexation of Crimea, which she has described as "unfair and silly."

It is a stance which contrasts markedly with Macron, a pro-EU, pro-integration candidate who has said he would keep sanctions on Russia in place, if not add to them.

While Macron has run as an independent centrist, Le Pen has campaigned, until recently, as head of the far-right National Front. She's faced criticism for the fact that her campaign was partly funded by a Russian bank. But she said she had no other choice, after French banks turned her down.

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Eyebrows were raised when Le Pen traveled to Moscow for a meeting with Putin last month.

Putin stressed the "great importance" of closer French-Russian ties following the meeting. And although the Kremlin insists it is not playing favorites in the French election, Le Pen's position on Russia is quite clear.

"Le Pen has been very open about her desire to have better relations with Russia -- she's an outspoken opponent of sanctions [against Russia], and she's interested in taking France outside of NATO," said Will Pomeranz at the Woodrow Wilson Center in Washington.

"She has a very populist right-wing message that plays to Putin's narratives -- it undermines Western institutions."

"Hacking"

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Tokyo-based cybersecurity firm Trend Micro says it discovered four phony Web domain names that were very similar to the domain names of the Macron campaign -- presumably to try to trick careless campaign workers into accidentally compromising their email accounts. For example, a fake domain called mail-en-marche.fr was set up on April 12. Macron's party is En Marche!

Feike Hacquebord from Trend Micro told CNN he could not say whether the hackers were Russian. But the report pointed the finger at a group called Pawn Storm -- also known as Fancy Bear -- a cyberespionage organization that other experts say is based in Russia and was behind the US election-related hacks.

Macron's digital campaign manager Mounir Mahjoubi confirmed there had been attempted hacks, but said they weren't successful.

A French official told CNN that French intelligence services are warning campaigns to take steps to prevent being targeted by hackers.

Russia has denied all accusations of being behind any hacking in France and the US.

Whether the attempted hacking will have any effect on the election race -- in which Macron leads Le Pen by as much as 20 points according to some polls -- is questionable.

Fabrice Epelboin, cybersecurity expert at Yogosha, told CNN that he believes the attempted hacks are unlikely to affect the election unless a truly staggering piece of information is revealed.

"Hacking is a big part of modern day politics," he said. "This is not the first time it has happened.

"With Russia, it comes down to the fact that Le Pen is pro-Russia and Macron is not, but these attacks shouldn't have an effect.

"Macron's team were really aware of the cybersecurity because of what happened with Hillary Clinton and John Podesta's emails.

"What happened to Clinton was basic hacking -- it wasn't technically impressive. It was basic."

"Fake news"

The hacking attempt may have failed, but Macron's campaign says it has been unable to shake off a steady stream of anti-Macron "fake news" stories emanating from websites it claims are linked to Russia.

"Two big media outlets belonging to the Russian state -- Russia Today [RT] and Sputnik -- spread fake news on a daily basis, and then they are picked up, quoted and influence the democratic (process)," Ferrand told Reuters. Both RT and Sputnik have denied the accusation to CNN.

Then, just this week, RT told CNN that Macron's campaign had pulled its its accreditation to cover campaign events withdrawn without explanation.

A spokesperson for the channel said it hoped that Macron's team "will see fit to afford the courtesy of accreditation shortly, and not attempt to curtail journalism, and manipulate the media, by selecting who can and can't report on his campaign."

The Macron campaign refused to comment when asked by CNN, but Reuters reports that a Marcon spokesman confirmed they'd barred access to the candidate. Russia's Foreign Ministry expressed outrage about the decision.

Russia's coverage of the election has caused consternation in France, particularly in the Macron camp.

In February, Russian newspaper Izvestia reported comments from Wikileaks founder Julian Assange, who claimed his organization, WikiLeaks, had "interesting information" about Macron.

France's polling commission issued a warning in early April after a Russian news report claimed that Francois Fillon -- a conservative politician with sympathetic views towards Russia -- was leading the presidential race, contradicting the mainstream domestic polls.

Professor Philip Howard at the Oxford Internet Institute told CNN that although the volume of misleading news on the French election falls short of a deluge, there is enough of it floating around to cause concern.

A study by University of Oxford researchers, which uses the term "junk news" to encompass disinformation and unreliable news, has found that French people are more likely to share real news on social media.

"Social media users in France shared many links to high quality political news and information -- roughly at a ratio of two links to professionally produced news for every link to other kinds of sources," the study found.

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As for the "other sources" referred to in the report, Howard says Russian outlets such as RT and Sputnik are two of the most prolific when it comes to spreading disinformation.

"Both RT and Sputnik belong in the junk category," Howard said. "They belong in the category which includes propaganda and a lack of fact checking."

"They use sensational photos, sensational titles and a lot of their content is commentary packaged as news.

"What we don't know is how well French voters can distinguish between junk and content."

RT told CNN that Howard's characterization of the network as junk news was "entirely baseless" and "disappointing."

Sputnik also defended its reporting, telling CNN it produces "reliable and high quality journalism."

"This helps us to counter-balance the 'one opinion allowed' policy of the mainstream media. We have faced similar accusations in the past and they always turn out to be untrue and completely fictitious; so if anything is 'fake', it is these accusations," a spokesman told CNN.

Where we're at

So far, the attempted hacking of the Macron campaign has failed to shift the balance of power ahead of the May 7 runoff.

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Le Pen, who has temporarily stepped down from her position as leader of the National Front, is attempting to broaden her appeal.

For many voters, it seems this election is about the desire for change, and disenchantment with a political class which many feel have left them behind. That was made evident in the rejection of the two main parties in their opening round of voting.

France is suffering from high unemployment, a stagnant economy, security worries, and remains bitterly divided. The government has struggled to cope with immigration and integration.

That has played into Le Pen's hands. Many of her supporters feel increasingly alienated by the so-called "political elite."

Those factors benefit Macron, too. He has projected himself as the country's future, a young and ambitious man who wants France to remain open and at the heart of Europe.

But whether Macron can emerge unscathed from the swirl fake news stories remains open to question, Howard says.

"There will be junk news purposefully designed to confuse voters, and some of it will spread like wildfire over social media networks," he said.

"Whether it has an impact on voters' decisions is difficult to know."