The couple have regularly featured in France's celebrity and lifestyle magazines since the telegenic Macron, 39, resigned as Economy Minister from the Socialist Government last northern summer to launch his bid for the presidency.
Macron has previously dismissed claims he is gay, but his latest comments may have been sparked by a report in the Russian Government-controlled news site Sputnik in which a French MP from Fillon's Les Républicains party said he was backed a "gay lobby".
Fillon, who until the financial scandal broke two weeks ago was the leading presidential candidate, was today seeking to get his campaign back on track after publicly denying the accusations and saying he was the victim of a smear campaign.
But his counter-offensive appears to have failed to win back public support, with the latest opinion poll confirming earlier surveys that showed around two-thirds of French people want him to stand aside and let another conservative candidate run.
Fillon served as Prime Minister from 2007 until 2012 under then President Nicolas Sarkozy, who today was ordered to stand trial over the allegedly fraudulent financing of his failed 2012 re-election campaign.
Opinion polls put Macron ahead of Fillon in the first round of the election in April, but only by a few percentage points, and behind Marine Le Pen, leader of the far-right Front National.
Only the top two candidates go through to a second round on May 7. Polls show that Macron would beat Le Pen with about two-thirds of the vote and that Fillon would win by a smaller, but still comfortable margin.
But many believe that all bets are off after the Brexit referendum and the presidential victory of Donald Trump in the US.