The EU parliament itself seems to have a procedure to use secret ballots in some cases:
Normally MEPs vote by show of hands, and the President of the sitting determines the majorities in each case. If the show of hands is unclear, the president calls for an electronic vote to secure a more precise result. A roll call vote must be taken if requested by a political group or at least 40 Members the evening before the vote. In this case, the individual vote cast by each MEP is recorded and published in an annex to the minutes, unless voting by secret ballot has also been requested.
As to specific countries, the EP published a document on voting by secret ballot in the Member State parliaments which seems to have the answer to your question:
Of the 20 Member State parliaments which took part in a survey carried out at the request of the secretariat of the Committee on Constitutional Affairs by the European Centre for Parliamentary Research and Documentation (ECPRD), 10, i.e. those in Austria, Belgium, the Czech Republic, Hungary, Italy, Latvia, Slovakia, Slovenia and Spain, make provision for secret ballots except where decisions involving persons, such as elections, appointments, etc., are concerned. Conversely, the parliaments of the 10 other Member States, i.e. those in Denmark, Estonia, Finland, France, Germany, Greece, Lithuania, Poland, Portugal, Sweden and the United Kingdom, may not employ secret ballots in similar circumstances.
It goes on to list the specifics in each relevant cases. To quote a few:
The secret ballot exists in the Bundestag only for elections (Rule 49 of the Rules of Procedure). The Bundesrat's Rules of Procedure do not provide for secret votes.
Voting shall be secret if so requested by fifty Senators at a Plenary Sitting or by one-third of the members of a committee.
Secret ballots are employed for appointments (election of the Presidents of the Chambers and of the Bureau).
The Rules of Procedure of both the Chamber of Deputies and the Senate limit secret ballots to votes on persons and on amendments to these Rules. More generally, they may be requested where votes touch upon the fundamental rights and liberties enshrined in the Constitution, the Senate extending this right to the rights of the family and of the person.
The Standing Orders contain no provision for vote by secret ballot in divisions of the House. In the House of Commons, with the exception of provisions for the election of the Speaker of the House, when there is more than one candidate, there are no provisions for secret ballots.
There might be a more recent version somewhere that covers the most recent batches of EU members.
As an aside, a thing to keep in mind is that whether legislatures should be using secret ballots or not was hotly debated in parts of Europe at one point. In contrast with the UK, the US, and former British holdings, where the practice of democracy was reasonably well established by modern times, a lot of Europe was introduced to parliamentary practice at gunpoint by Revolutionary France. And it was quite a time...
As explained in this paper that goes through France's debate on the topic specifically, French MPs initially voted in public. But in the days of the French Revolution, it ended up meaning MPs got pressured, catcalled, threatened by mobs, or worse. The MPs complained that, because their votes were public, they couldn't play their proper role as elective representatives and vote with their conscience. Which, in plain English, meant they didn't want to get guillotined because of their voting record.
As a result, French MPs ended up using secret ballots for a few decades. It was only later in the 19th century, when the dust had settled and democratic practice was more established, that the use of secret ballots in the French parliament got repelled.