You shouldn’t need a visa to travel to the EU after Brexit. The European Commission announced in November 2018 that, even in a no-deal scenario, UK travellers can still visit the EU without a visa, providing the same is offered to European citizens visiting the UK. The European Commission has said that from 2021, UK citizens will need to pay a fee (of around 7 Euros) for this visa exemption. This is part of a new electronic travel authorisation system applying to all third country visitors to the EU, similar to the US ESTA system.
The UK government and ABTA have also put together some useful information about holidaying in the EU after the proposed leave date (currently 29th March 2019). These resources can be found below:
Guidance for UK nationals travelling to the EU: https://www.gov.uk/guidance/uk-nationals-travelling-to-eu-essential-information
Passport validity checker: https://www.passport.service.gov.uk/check-a-passport
ABTA Advice for travellers: https://www.abta.com/tips-and-advice/brexit-advice-for-travellers
The UK Government has launched a ‘Get Ready For Brexit’ campaign - further details can be found here.