My spouse has just passed away. Do I need to file an inheritance tax return even though I am exempt from inheritance tax?

It depends. The surviving spouse is indeed exempt from inheritance tax (Article 796-0 of the French General Tax Code).
However, the law requires heirs, including the surviving spouse, to file an inheritance tax return when the gross value of the estate exceeds €50,000. Conversely, if the gross estate value is below €50,000 and your spouse had not made any gifts or manual donations that were neither declared nor registered, you are exempt from this obligation (Article 800 of the French General Tax Code).