Trump drew France's François Delattre aside during a working lunch for UN ambassadors and questioned him on the first round's outcome.
"I brought him up to date on the situation, putting things in perspective," the French ambassador told the AFP news agency.
Sunday's vote has resulted in former economy minister Emmanuel Macron facing the National Front's Marine Le Pen in the second round on 7 May.
Le Pen was the only well-known French politician to welcome Trump's election last year, hailing his economic protectionism and hostility to immigration.
Following last week's murder of a police officer on Paris's Champs Elysées, Trump commented that the attack would "probably help" Le Pen because “strongest on borders and she's the strongest on what's been going on in France”.
Le Pen came in second on Sunday, with 7,679,493 votes compared to his 8,657,326.
The lunch was related to the US presidency of the UN Security Council in April.
Having dismissed the UN as "just a club for people to get together, talk and have a good time" during the US election campaign, Trump signaled that he was ready to work with it if the world body shows that it can reform and become more responsive to global crises.