If the UK leaves with a deal, travel to the EU will remain the same as now until at least 31 December 2020. You will not need to apply for a visa to travel or work in the EU during this time.
If the UK leaves the EU without a deal, the rules for travelling or working in Europe will change after the day they leave.
The European Commission has proposed that in a no deal situation, if you’re a British Citizen, you would not need a visa for short stays in the Schengen area or elsewhere in the EU. You would be able to stay for up to 90 days in any 180-day period. Visits to the Schengen area within the previous 180 days before your date of travel will count against the 90-day limit.
On arrival in the Schengen Area, you may be asked to confirm that you have sufficient funds available for the duration of your stay. As non-EEA nationals, different border control checks will apply, and you may also be asked to show a return or onward ticket. UK nationals would not have an ongoing right to use the separate lanes provided for EU, EEA and Swiss nationals.
The 90-day visa-free period does not entitle you to work in the Schengen area. Most countries will require a visa and work permit.