"It is inconceivable that personal considerations, which can constitute elements of pressure, should get in the way of a minister's action, especially one that negotiates regularly with the United States on issues of utmost importance," wrote the Front National in a press release on Friday.
In this light, the far-right party considers that Laurent Fabius should resign to allow someone else to take up the job of foreign minister in "total serenity".
Fabius senior doesn't appear to have had much of that. The day he was appointed as number two of the French government - on May 16 2012 - his son Thomas was living it up in a Las Vegas casino. So much so, that he contracted huge debts totalling more than $3.5 million (3.2 million euros), that he tried to mask by writing bad checks.
Some of the checks written were from French banks like Société generale. They bounced due to insufficient funds, and now the US wants its money back.
A warrant for Fabius’ arrest was issued back in April 2013, but it's only just been revealed now in the French press by magazine Le Point.
The gambler risks arrest if he sets foot in the United States, a spokesman for Nevada's Clark County told news agency AFP.
Fabius, 33, who heads a financial consulting firm, has been reported to have spent millions of dollars in casinos in the past and was investigated in 2013 for fraud and money laundering over a shady real estate deal.
The news of his arrest warrant is unlikely to go down well with the French public, who are very suspicious of outlandish displays of wealth, especially at a time of financial hardship.
On Friday, business and worker unions are set to sit down together to discuss new plans to extend the length of work required to qualify for a full pension.
Some will disapprove of the idea of being asked to work longer, when government ministers' sons can blow sums they'll never see in a lifetime, within hours.