Natalie Ficero is Professor at the University Cote d’Azur specializing on law of justice, civil procedure and mediation. She is member of the French High Council for the Judiciary and works as an independent expert for the Council of Europe.
Based on the freedom of expression and the right to information, social networks, open databases of court decisions and their algorithmic processing allow to find a lot of personal data of judges. However, French law sets limits to the publicity of judgments, in order to guarantee the security and privacy of judges. "When its disclosure is likely to undermine the security or privacy of these persons or their entourage, any element that could identify the parties, third parties, judges and members of the court registry is also concealed." 
French law considers that the limits also result from the rules of ethics for magistrates.  In particular, the code of ethics imposes on magistrates an obligation of prudence in the use of social networks (even if they use a pseudonym), which makes it possible to limit the information on their personal life, to preserve the image of justice and the image of impartiality. The High Council for the Judiciary has already issued disciplinary sanctions against magistrates who used social networks in an inappropriate manner. Also, the French Ministry of Justice published an information sheet indicating good practices on the subject.
At times, the information available on judges can lead to judges being profiled, including by using machine learning applications, in order to predict their judgments. This can raise ethical dilemmas from the standpoint of the right to a fair trial, impartiality, fairness and judicial integrity, among other issues. French law explicitly prohibits the "profiling" of judges. "The identity data of judges and members of the registry may not be reused for the purpose or effect of evaluating, analyzing, comparing or predicting their actual or supposed professional practices." Both penal and administrative measures and sanctions are available. 
Nevertheless, the principle of transparency of justice remains and the parties must have access to the identity of the judge, unless the judge can justify a risk of infringement of their security and privacy. Moreover, it does not seem conceivable to prohibit litigants from "googling" the judge.
There exist some good practices and ideas on how the public knowledge of judge-related data can be balanced to strengthen public confidence in the judicial institution and judicial integrity, while at the same time protecting the privacy of judges and eliminating any potential integrity-related risks. In particular, the following could be considered:
 See Art. L. 111-13 of the Code of Judicial Organization (Code de l’organisation judiciaire), https://www.legifrance.gouv.fr/codes/id/LEGITEXT000006071164/ (last visited on 19 July 2022)
 In France, « magistrate » refers to judges and prosecutors. Judges and prosecutors belong to the same body. The French High Council for the judiciary (“Conseil supérieur de la magistrature”) is responsible for their appointments and their discipline.
 See Art. L 111-113 of the Code of Judicial Organization.
 See Art. 226-18, 226-24 and 226-31 of the French Criminal Code and Law No. 78-17 of 6 January 1978 relating to data processing, files and freedoms.