Many restrictions persist, however, and it is unclear how keen Europeans will be to travel this summer.
The continent is still closed to Americans, Asians and other international tourists.
The European Union's 27 nations, as well as those in the Schengen passport-free travel area, which also includes a few non-EU nations such as Switzerland but not the UK, are not expected to start opening to visitors from outside the continent until at least the beginning of next month, and possibly much later.
Britain, which left the EU in January but remains closely aligned with the bloc until the end of this year, only last week imposed a 14-day quarantine requirement for most arrivals, horrifying its tourism and aviation industries.
As a result, France is asking people coming from Britain to self-quarantine for two weeks and several other nations are not even letting British tourists come in during the first wave of reopenings.
Anyone coming in to the UK from abroad (apart from those arriving from Ireland) must self-isolate for two weeks.
Announcing Monday's reopening of borders and Paris restaurants, French President Emmanuel Macron said it is time "to turn the page of the first act of the crisis" and "rediscover our taste for freedom".
But he warned: "This doesn’t mean the virus has disappeared and we can totally let down our guard...
"The summer of 2020 will be a summer unlike any other."
Even inside Europe, there is caution after more than 182,000 virus-linked deaths.
Europe has had more than two million of the world's 7.9 million confirmed infections, according to a tally by Johns Hopkins University.
"We have got the pandemic under control, (but) the reopening of our frontiers is a critical moment," Spanish Prime Minister Pedro Sanchez said on Sunday as he announced that his hard-hit country is moving forward its opening to European travellers by 10 days to June 21.
"The threat is still real. The virus is still out there," he said.
Still, the need to get Europe’s tourism industry up and running again is also urgent for countries such as Spain and Greece as the economic fallout of the crisis multiplies.
Greek Prime Minister Kyriakos Mitsotakis acknowledged that "a lot will depend on whether people feel comfortable to travel and whether we can project Greece as a safe destination".
In a trial run, Spain is allowing thousands of Germans to fly to its Balearic Islands starting on Monday - waiving its 14-day quarantine for the group.
The idea is to test out best practices in the coronavirus era.
"This pilot programme will help us learn a lot for what lies ahead in the coming months," Mr Sanchez said.
"We want our country, which is already known as a world-class tourist destination, to be recognised as also a secure destination."
Europe's reopening is not a repeat of the chaotic free-for-all in March, when panicked, unco-ordinated border closures caused traffic jams that stretched for miles.
Still, it is a complicated, shifting patchwork of different rules, and not everyone is equally free to travel everywhere.
Several countries are not opening up yet to everyone.
Norway and Denmark, for example, are keeping their borders closed with Sweden, whose virus strategy avoided a lockdown but produced a relatively high per capita death rate.
Cars queued up on Monday morning at some crossings on the German border with Denmark - which is now letting in visitors from Germany but only if they have booked accommodation for at least six nights.
With flights only gradually picking up, nervousness about new outbreaks abroad, uncertainty about social distancing at tourist venues and many people facing record unemployment or pay cuts, many Europeans may choose simply to stay home or explore their own countries.
German Chancellor Angela Merkel and Austrian Chancellor Sebastian Kurz are both planning to holiday in their homelands this year.
"The recommendation is still, if you want to be really safe, a holiday in Austria," Austrian foreign minister Alexander Schallenberg told ORF television, recalling the scramble in March to bring home thousands of tourists as borders slammed shut.
"In Austria, you know that you don’t have to cross a border if you want to get home, and you know the infrastructure and the health system well," he said.
The German government, which helped fly 240,000 people home as the pandemic grew exponentially, also has no desire to repeat that experience.
"My appeal to all those who travel: enjoy your summer holiday – but enjoy it with caution and responsibility," German foreign minister Heiko Maas said.
"In the summer holidays, we want to make it as difficult as possible for the virus to spread again in Europe."
The Dutch government said its citizens can now visit 16 European nations, but urged caution.
"You can go abroad for your holiday again," foreign minister Stef Blok said.
"But it won’t be as carefree as before the corona crisis. The virus is still among us and the situation remains uncertain."