The arch-federalist former Belgian PM, who this year published a book calling on EU states to forge "a more flawless Union", warned last week Britain could lose its rebate and opt-outs if it changes its mind and decides to stay.
Both sides are still in disagreement over how exactly they will progress.
Speculation has also mounted that she could now seek a softer Brexit, which involves staying in either the EU's single market or customs union.
"Now, the hard work begins", Mr Davis said, adding he wanted a deal that worked for both sides.
The so-called Brexit bill is likely to be the biggest hurdle in the early negotiations.
Speaking at the Elysee Presidential Palace, Macron stated that once the process to leave the 28-member bloc started, the rest of the European Union members should be collectively clear that it would be harder to reverse such a course.
As has been the case throughout the run-up to the official talks, the main emphasis of the preview was on the U.K.'s desire to secure a future relationship with the EU.
Threats by Britain to walk away without a deal have also anxious European capitals.
The British team includes the Permanent Secretary at the Department for Exiting the European Union (DExEU) Olly Robbins, Phillip Rycroft, the department's Second Permanent Secretary and Simon Case, the newly appointed Director-General of the UK-EU Partnership.
- June 22 - Mr Barnier reports back to the leaders of the EU27, who are expected to endorse a process for relocation of European Union agencies now based in the UK.
Working groups will discuss aspects of the negotiations in the afternoon before a final meeting between Mr Davis and Mr Barnier.
Britain's negotiators came to Brussels seeking a "new, deep and special partnership with the European Union" on Monday as talks on the unprecedented British withdrawal from the European Union finally got under way.
Davis and Barnier have one key issue over the first weeks of talks: building trust after months of haggling over leaks and figures over the final bill that Britain would have to pay for leaving.
The UK chancellor said he would not agree to a deal that would "destroy" Britain just hours before the official Brexit negotiations begin.
While Barnier insists on the "sequencing" of talks, so that trade negotiations can not start until probably January, finding a way to avoid a "hard" customs border for troubled Northern Ireland may well involve some earlier discussion of the matter.
Mr Hammond told the BBC's Andrew Marr Show that having no deal would be "a very, very bad outcome for Britain" but added that one that aimed to "suck the lifeblood out of our economy over a period of time" would be even worse.