The web presents unprecedented opportunities for large-scale collection of text in many languages. However, two critical steps in the development of web corpora remain challenging: the identification of clean text from source HTML and the assignment of genre or register information to the documents. In this paper, we evaluate a multilingual approach to this end. Our starting points are the Swedish and French Common Crawl datasets gathered for the 2017 CoNLL shared task, particularly the URLs. We 1) fetch HTML pages based on the URLs and run boilerplate removal, 2) train a classifier to further clean out undesired text fragments, and 3) annotate text registers. We compare boilerplate removal against the CoNLL texts, and find an improvement. For the further cleaning of undesired material, the best results are achieved using Multilingual BERT with monolingual fine-tuning. However, our results are promising also in a cross-lingual setting, without fine-tuning on the target language. Finally, the register annotations show that most of the documents belong to a relatively small set of registers, which are relatively similar in the two languages. A number of additional flags in the annotation are, however, necessary to reflect the wide range of linguistic variation associated with the documents.