Yes. Jainism does not restrict becoming Jain by ethnicity or nationality. A European (or anyone from anywhere) can become Jain by embracing Jain teachings and practices, and by taking the appropriate vows.

Key points:

• For lay followers (Shravak/Shravika): adopt the core Jain vows, especially non-violence (ahimsa), truthfulness (satya), non-stealing, celibacy in thought/word/behavior, and non-possessiveness (aparigraha). Regular practice includes study, meditation (samayik), vegetarianism, and ethical living.
• For formal initiation as a Jain monk/nun (diksha): this is a traditional, more involved path within a Jain lineage. It is extremely rare for Westerners and typically requires guidance from a Jain guru or monastic community and strict adherence to monastic rules. Most Western practitioners pursue lay Jainism rather than full monastic initiation.
• Traditions differ: Digambar and Shwetambar communities may have different rites or emphases, but both accept converts and emphasize sincere practice of the dharma.
• Community support: living temples or Jain centers in Europe can provide instruction, guidance, and opportunities to participate in sadhanas and festivals.

If you’d like, I can share concise steps for starting as a lay Jain or point you to Jain Knowledge resources about Jain vows and daily practices.