Ostensibly, the two may not have much in common. Typically for a French career politician, Mr Barnier is a product of the 'Grandes Ecoles', the ultra-elitist part of France's higher educational system; in addition, he's a passionate skier. Somehow, I can't imagine Mr Davis - the child of a single mother and brought up on a south London council estate - is into skiing (although you never know - he spent part of his career with Tate & Lyle working in Canada). However, his MBA from the London Business School tells us that he, too, sampled education at the highest level.
So maybe there is some common ground, which could be important because the consensus is that the UK's team needs all the help it can get. The EU's bureaucracy seems to have a clean grasp of both the exit procedure and the EU's aims, while the UK's team gives the impression it hasn't yet got around to booking its tickets for Monday's early-morning Eurostar to Brussels.
All this is a way of saying that - while it was remarkable how Brexit barely figured in the general-election campaign - it will move to centre stage in the coming weeks. For readers whose capital is primarily tied up in UK assets - both property and equities - that's not a reassuring prospect.
Their chief thought may be how to hedge all that exposure to sterling. Many equities - especially those in internationally-orientated FTSE 100 companies - offer defacto hedging as a function of where they trade. Beyond that, currency hedging - most likely via exchange traded funds - should be a feature of every portfolio anyway. If it isn't, fix that; but not via exposure to the euro - that remains the one major currency I wouldn't touch with a barge pole.
It's not that the euro faces existential threats. If it did, that would hardly be a cause for glee on this side of the English Channel. After all, if the eurozone fell apart, the collateral damage to the UK's economy would hardly bear contemplation. The best that could be hoped for is that the resultant surge in whatever became Germany's currency would help to cut the £25bn annual deficit in the UK's trade with Germany. But such a cut would have everything to do with the stability of depression and nothing to do with the liveliness of the UK's post-Brexit economy.
Yet the threats don't have to be existential for the currency to be shunned because it is so obvious that the euro zone remains home to crises both to be repeated and still to come. It is almost axiomatic that the Greek crisis will have a re-run, although - happily - it is assumed that Greece's economy is too small for its crises to pose fatal threats - its output is just 5 per cent of Germany's.
That has not prevented Greece's earlier crises from seeming damn-near existential, which says much about the inability of the eurozone to act quickly and decisively in a common interest. That is likely to persist while national interests continue to trump the 'common interest', whatever that might be. Perhaps that can only be discovered in the refining heat of catastrophe. In which case, bring on the Italian crisis, the one involving the EU's fourth-largest and the world's 12th-largest economy, which has been waiting to happen for years.
The weight of public sector debt in Italy is a source of anxiety since, globally, only Japan and Greece bear a heavier burden. Italy's commercial banking sector may be in a worse state; at least, the denial of non-performing loans has been on a scale not seen since Japan in the 1990s. Yet there are signs this is changing. At Italy's - and the world's - oldest bank, Monte dei Paschi di Siena, the EU has agreed a state bailout. As with these things, much fudge is involved since retail bondholders had to be saved from the wipeout that shareholders faced. That done, Monte dei Paschi could be viable, as could the country's biggest bank, UniCredit, which is fresh from a capital injection.
That still leaves other creaking banks and - maybe worse - a dysfunctional economy that refuses to grow. Italy's productivity, as measured by output per head, is still the same as it was in 2000, whereas, across the average of the G7 group of wealthy nations, it has grown by almost 20 per cent.
As I say, these are reasons to shun the euro - for hedging purposes, the US dollar and the Swiss franc look far more appropriate. However, they are not reasons to be optimistic that the UK's Brexit negotiations can go well because, in effect, both sides are as weak as each other. Ultimately, the two sides are not playing a zero-sum game except, perhaps, in the headline-grabbing side show that will be about the size of the UK's 'divorce settlement'. So it is a concern that the UK government has yet to show any appreciation of this. All the more reason therefore that Mr Barnier and Mr Davis should hit it off.
