Image copyright Getty Images

On Friday morning Donald Trump dipped his presidential toe into French electoral politics, tweeting about the possible impact of the Paris shooting on Thursday that resulted in one police officer dead and two seriously wounded.

"Another terrorist attack in Paris," Mr Trump wrote. "The people of France will not take much more of this. Will have a big effect on presidential election!"

The previous day, during a joint press conference with Italian Prime Minister Paolo Gentiloni, Mr Trump had quickly labelled the incident a "terrorist attack" - before even French authorities had done so.

"It's a very, very terrible thing that is going on in the world today," Mr Trump said. "And what can you say? It just never ends. We have to be strong and we have to be vigilant, and I've been saying it for a long time."

That last line is certainly true.

Media playback is unsupported on your device Media caption See how events in Paris unfolded

While the dynamics of French politics are decidedly different from those in the US, Mr Trump may recall that another incident in Paris - the November 2015 mass shooting at the Bataclan theatre - helped solidify his lead in the polls leading into the Republican presidential primaries.

"Everyone is now saying how right I was with illegal immigration and the wall," he tweeted several days after the attack two years ago. "After Paris, they're all on the bandwagon."

Mr Trump did not mention her by name, but the president seems to be predicting the Champs-Elysees shooting will be a boost for French nationalist candidate Marine Le Pen, who has campaigned on deporting suspected Islamic militants and a French withdrawal from the European Union.

Media playback is unsupported on your device Media caption The five main candidates are (L-R) Jean-Luc Melenchon, Benoit Hamon, Emmanuel Macron, Francois Fillon and Marine Le Pen

Although Mr Trump has not formally met the French presidential candidate, she is close to some of the same advisers who helped craft the president's populist message during his campaign last year and was spotted in Trump Tower during the presidential transition in January.

Breitbart News, which was an early supporter of Mr Trump's improbable presidential bid, has also warmly covered Ms Le Pen's efforts.

"A new world is emerging, global equilibriums are being redefined by the fact of Trump's election," Ms Le Pen said the day after Mr Trump's presidential victory. "Their world is crumbling; ours is being built."

While critics may view Mr Trump's Friday morning tweet as an unwelcome effort to influence the politics of another nation, the reality is slightly more complicated than that. Earlier on Thursday former President Barack Obama spoke with another leading French candidate, Emmanuel Macron, who has campaigned in favour of a strong European Union and open borders.

Media playback is unsupported on your device Media caption Marseille voters tell us if their voting intentions have changed after a gunman killed a policeman in Paris

"The main message I have is to wish you all the best in the coming days." Mr Obama said in an edited video of the call that Mr Macron posted on Twitter. "And make sure, as you said, that you work very hard all the way through because you never know, it might be that last day of campaigning that makes all the difference."

"Let's keep defending our progressive values," Mr Macron wrote. "Thank you for this discussion @BarackObama".

In other words, the French election - from an American perspective, at least - could be setting up a proxy battle between the current and former president and their competing views of economic nationalism versus liberal globalism.

A similar dynamic played out during last June's Brexit referendum in the UK, when Mr Obama tacitly endorsed the Remain camp, while Mr Trump heralded the Leave victory as evidence that his nationalist politics were gathering strength.

Now, after two notable defeats for the existing international establishment - in Brexit and Mr Trump's November election - Mr Obama may view Mr Macron as a last, best hope to stem a rising populist tide in the West. Although European Union supporters were heartened by the results in the recent Dutch elections, where nationalist candidate Geert Wilders was defeated, the French vote is a much more significant matter.

Mr Trump and his advisers may view Ms Le Pen as the hand that will deliver a death blow to the European Union and cement his own election as more than a quirk of American politics and, instead, as the harbinger of a new global order.

You can follow the first round of the French election on the BBC News website. Click here for all our latest coverage. On the day of the election, we will be running a live page bringing together the latest news, video and analysis.

On TV, you can watch a BBC World News Election Special, from 18:30 BST (17:30 GMT / 19:30 local time in France) on Sunday, which will be broadcast on BBC News in the UK and on BBC World News internationally, with Christian Fraser presenting from Paris.

For radio, BBC World Service will broadcast a special extended edition of Newshour from Paris at 18:00 GMT on Sunday.