The offer came during a telephone conversation between the leaders during which Macron congratulated Johnson on becoming head of the British government.
Johnson was elected leader of the ruling Conservative party on Wednesday following the resignation of Theresa May.
On Thursday Johnson told British lawmakers that he wanted the European Union to rethink its opposition to renegotiating a deal on how Britain would leave the bloc.
Johnson said that if the EU did not want talks, he would withdraw Britain without a deal on 31 October.
Macron has emerged as one of the EU leaders most willing to see Britain leave soon, without a deal if it chooses, so as not to threaten EU stability and unity.
Amélie de Montchalin, France's minister for European affairs, told the TV station France 2: "We want to work with Boris Johnson and we need to do that. Britain is a partner and will remain a partner after Brexit. It is a country that is close to us."