Le Grand Secret (1989).
Professor Bahanba, an Indian scientist also working on a cancer treatment, has discovered JL3, an immortality serum that stops aging and eliminates vulnerability to disease in any living being. [...]
Jeanne learns that Samuel, now known as Colonel Bass, is on an island called 307, which is guarded day and night by the army. The island hosts a self-sufficient community led by Professor Bahanba, who also acts as the community's spiritual guide. Jeanne, now fifty years old, travels to the island and finds Roland, who is still a spirited young man of thirty. Their love is not what it once was and Jeanne finds herself unable to contract symptoms.
The French version of the Wikipedia page ends with (translation courtesy of DeepL):
On Islet 307, the young stop growing old at 18 years old, the women have to take medication to avoid being fertilized, the animals also undergo the same treatments except for insects whose high reproduction rate forces them to be eliminated regularly. Harmony seems to reign, suffering and tensions annihilated. Yet the sexual instinct remains the most vivid and young people have a violent desire to procreate. A young couple, Han and Annie, Roland's daughter, break the rules and set an example that leads to an upsurge in pregnancies.
Tensions begin to appear between adults who want to keep their balance at all costs and teenagers who rebel, especially since another virus, C14, is apparently able to counteract the effects of JL3. The death of Professor Bahanba, who let himself starve to death because of his Hindu beliefs, precipitated the disunity of the island's inhabitants. A war broke out, causing the island to be set ablaze and then destroyed by the governments. Only Han and Annie manage to escape...
Found with the Google query
miniserie televisee immortalité ile tests nucleaires (
tv miniseries immortality island nuclear tests). Your mention of it being European made me think it could be French, since France produced a couple of such sci-fi miniseries back in the 80s.