Yes, you should be able to, definitely to France. Check for other countries.
(I registered in this system just to send you this link but apparently the system doesn't allow me to post links. Kind of useless as a service).
France in the United Kingdom, Consulate General website says:
The foreign spouse of a EU national (except French national) may enter France without visa if holding:
- A valid travel document;
- A valid UK residence permit with the endorsement "family member of EEA national" (this endorsement is compulsory to be visa exempted);
- and if they are joining or travelling with the EU national.
If you do not satisfy the above conditions, you will need to apply for a visa to travel to France (for instance if your residency is not explicit or if you are travelling to France for business).
Note that children and parents of EU Nationals still require visas to travel to France. It’s also the case for the spouses of British citizens as their residence permit does not bear the endorsment " family member of EEA national" as required by the art. 10 of the European Council/Parliament Directive 2004/38 CE.
Be advised that if you are unable to provide the requested documents to obtain a visa as the spouse of an EU citizen, you willneed to lodge an application for a short stay Schengen visa, i.e. pay the visa administrative fees and produce all requested supporting documents.
(source: Ambafrance)
