When are European borders expected to be open for non-European tourists? I am planning to travel at the end of October.
What the last months revealed is how difficult that will be and how little coordination there is in this matter. Schengen countries (which include 7 of the top 10 tourism destinations in Europe by number of international visitors) worked out some agreement to try to resume some sort of common policy in this respect but individual countries still took a lot of ad hoc measures, some of which have been rolled back pretty quickly following an increase in Covid-19 cases.
Many governments (re)introduced measures like mandatory tests and quarantines for travellers going from (some part of) one European country to the next. Those are seldom enforced at the border but would still make cross-border movement more difficult. Planning a trip in October therefore seems very risky.
If you still choose to book a trip, Where can we find frequently updated details about travel/entry restrictions due to Coronavirus (nCoV-19)? list many useful ressources you could peruse to assess the situation before leaving. Always check your own country's foreign official travel advice, as it will often provide details on the rules that apply abroad to their citizens and/or residents and also inform you of any requirements that might apply when you come back.