Barnier, 65, who has been a minister in three French governments, says he wants a "win-win agreement" following the UK's referendum vote to quit the EU.
Some of the British media hailed his appointment by Commission chief Jean-Claude Juncker a "declaration of war" because Barnier clashed with City of London bankers during a 2010-14 stint as EU financial services commission.
But British Prime Minister Theresa May has said she is keen to work with him.
That may not be any day soon, since the EU says it will not negotiate until Britain has triggered the now famous article 50 of the Lisbon Treaty, which formally starts a two-year withdrawal procedure.May has said she does not expect to do that before the beginning of 2017.
400-strong Brexit task force
Barnier will head a Brexit task force, which could be 400-strong, and his deputy is German Commission trade official Sabine Weyand.
He is already caught up in an EU turf war with member states calling for talks to be conducted by the European Council, which groups the 28 EU leaders under former Polish prime minister Donald Tusk, rather than the Commission.
The Council has named Belgian diplomat Didier Seeuws as its negotiator, while the European Parliament, which is backing the Commission, also has its own negotiator, former Belgian prime minister Guy Verhofstadt.
Working on humour
On Thursday Barnier held "constructive" talks with German Foreign Affairs Minister Franck-Walter Steinmeier and is to tour other European capitals during the autumn.
London will not be among them, although he is acquainted with UK negotiator David Davies as both were Europe ministers for their countries in the 1990s.
Despite the EU's refusal to negotiate before article 50 is invoked, there are likely to be informal contacts with the British ambassador to the EU.
French politicians consider Barnier a hard worker but consider him deficient in the humour department, according to a profile in Le Figaro.
He told the right-wing paper that he is working on his sense of humour.