Check the exemption first
Article 4(5) of the Directive exempts microenterprises providing services from the accessibility requirements entirely. A microenterprise is under 10 people and under €2 million turnover or balance sheet total.
That is genuinely most independent restaurants, cafés and bars, and it is the first thing to establish, because the rest of the Directive is a substantial piece of work and there is no reason to do it if it does not apply.
The count is of the undertaking, not the site. A group operating six venues under one company is not a microenterprise because each venue has four staff.
If you are not exempt
The requirements sit in Annex I and, for services delivered through a website or app, amount to making the content perceivable, operable, understandable and robust. In practice conformance is demonstrated against EN 301 549, which for web content maps onto WCAG 2.1 Level AA.
For a venue that means the booking flow specifically: usable by keyboard, labelled form fields, sufficient contrast, error messages that say what went wrong, and content that works with a screen reader. The marketing pages matter less than the part where someone actually books a table.
You also need an accessibility statement describing how the service meets the requirements.
Why an exempt venue might do it anyway
Roughly a quarter of adults in the EU have some form of disability, and the numbers rise sharply with age. A booking form that cannot be completed by keyboard, or that puts pale grey text on white, loses bookings from people who would happily have eaten with you.
The overlap with ordinary quality is also large. Real form labels, visible focus states and readable contrast make the flow better for everyone using a phone in bad light, which is most people booking a restaurant.
There is no obligation here for an exempt venue. It is a straightforward commercial argument, and it should be made as one rather than dressed up as compliance.