Mr Macron, who arrived in the capital on Sunday, is the first western leader to arrive in the UAE to pay respect.
On social media, he said he was in Abu Dhabi to "pay tribute to the memory of Sheikh Khalifa".
He said Sheikh Khalifa was respected by all for the values of peace, openness and dialogue, and he pledged full support for President Sheikh Mohamed and the Emirati people.
They included Sultan Haitham of Oman, Jordan's King Abdullah II, Egyptian President Abdel Fattah El Sisi and Barham Salih, the Iraqi president, and Mustafa Al Kadhimi, the Iraqi prime minister.
Sheikh Mohamed also received the condolences of the UK's Prince Charles and Lloyd Austin, US Secretary of Defence.
During separate phone calls, the heir to the British throne and Mr Austin offered their heartfelt condolences and solace to Sheikh Mohamed and the Emirati people on the death of Sheikh Khalifa.
Prince Charles and Mr Austin also congratulated Sheikh Mohamed on his election as UAE President and wished him good luck as well as further progress and prosperity for the UAE under his leadership.
Sheikh Mohamed extended thanks and appreciation to Prince Charles Mr Austin for their warm feelings towards him, the UAE and its people.