Yes, travel insurance is worth carrying for a trip to Strasbourg, and while the city itself is a low-risk, well-developed destination, seat of the European Parliament and the Council of Europe, the honest reasons to carry cover here are seasonal crowding and onward travel into the Vosges rather than any real danger in the city.
Strasbourg has its own major university hospital and handles serious cases locally without the referral chain some other entries in this guide need, so the medical picture is genuinely reassuring for a European capital city. What still matters is checking whether your existing health cover extends abroad and specifically to France, since the rules differ sharply for EU residents and visitors from further afield, and this page cannot determine which applies to you.
Strasbourg's Christmas market, one of the oldest and largest in Europe, draws heavy crowds from late November through December, and the resulting congestion raises the everyday odds of lost belongings, pickpocketing, or a missed train connection more than any unusual seasonal danger. Trip-delay and belongings cover is worth checking if your visit falls in this window, alongside standard medical protection for the rest of the stay.
Many visitors continue on from Strasbourg into the Vosges mountains for hiking in summer or skiing in winter at resorts like La Bresse, and that onward leg carries its own real risk that the city portion of a trip does not - check that your policy names hiking or winter sports specifically rather than assuming a city-trip policy already covers mountain activity further out.
Keep any clinic paperwork, police reports for lost or stolen belongings, and receipts for delayed travel if the Christmas market crowds disrupt a connection. Many policies treat theft and delay as separate claim categories with their own documentation requirements, so check the wording before you travel rather than after something goes missing in the crowd.