While Westminster has "Hansard", and the US Congress has the "Congressional Record" - the European Parliament has "Verbatim Reports of Proceedings.
Producing a useable verbatim record is more complicated than for National Parliaments - the European Parliament allows speeches in any of the twenty four official languages of the the European Union. [English remains an official language] While there are translators in the chamber to give a simultaneous translation to people in the chamber; visitors and those watching the live feed of Plenary sessions - the official record takes longer to produce.
A first copy is available called the "Rainbow Edition". This records contributions in the language of each person speaking. Initially only a PDF version is available, but a few days later there is an HTML version - which allows searches.
The "Final Edition" is produced a little later. Again - it is in the languages used by whoever is speaking.
To search for a particular plenary session go to EP Verbatim Reports of Proceedings - the first part of this page covers the current plenary session, but if you scroll down you'll find "Search Verbatim Reports". This gives access to any of the Parliamentary debates from 1994. If you have a specific sitting you want to look at - enter that date in both boxes (Sittings from...to). Click on any of the individual results - and the next page give you the option to choose "Full Text". That will break the sitting down into individual items of business.
You can watch a video of each speech, The full Verbatim Report can be downloaded as a PDF - it's a big document (February 10th 2021 is a file of 3590k and 162 pages ).
Watching the video of the speech (an example can be seen here) allows you to choose which language you listen to. - but there is a disclaimer "The interpretation does not constitute an authentic record of proceedings." Alternatively copy and paste the speech in the Verbatim Report into Google Translate