Does a non-EU Spouse of a UK national need a visa to visit the Schengen area?

1. Yes, your wife does need a Schengen visa (only one visa for both countries). The “Right of entry” is defined thus in article 5 of the free movement directive (directive 2004/38/EC):

   2. Family members who are not nationals of a Member State shall only be required to have an entry visa in accordance with Regulation (EC) No 539/2001 or, where appropriate, with national law. For the purposes of this Directive, possession of the valid residence card referred to in Article 10 shall exempt such family members from the visa requirement.

   So the visa exemption only applies to family members with a “residence card referred to in Article 10”, which is a “Residence card of a family member of a Union citizen”. Unless you used the Surinder Singh route and your wife’s permit explicitly says “family member of a Union citizen”, it would not be the case for the spouse of a British citizen in the UK. See also Travel documents for non-EU family members on europa.eu.

   One difference is that the visa application does not require as much supporting documentation (some fields on the Schengen visa application form can be left empty) and it should be quick (the 15 days mentioned in @Max’s answer) and free of charge (but beware of outsourcing companies like TLS Contact and VFS Global, you might have to circumvent them and reach the consulate directly to avoid their “service charge”). The UK itself does not really follow this prescription as applications for EEA family permits can take a very long time but France mostly does, as far as I know.

2. It might be possible to apply for the visa at the border but I would expect some resistance from the border guards and significant delay. The Schengen visa code does provide for visas to be issued at the border in “exceptional circumstances”, especially if you show it wasn’t possible to obtain one before because of some emergency.

   Furthermore, the free movement directive provides that “Member States shall grant such persons [family members to whom the directive applies] every facility to obtain the necessary visas”, which is a bit vague but has been interpreted as meaning that third-country family members should be given an opportunity to prove they are covered by the directive before turning them back (in particular, that’s the take of the EU Commission in its Handbook for the processing of visa application and the modification of issued visas, which is not necessarily legally binding but at least somewhat official). Residing in the UK is not even necessary.

   Still, if that’s possible at all, applying at a consulate seems much safer/easier.

   (You have mentioned in point 1 that your wife would be travelling with you. I assumed you did not repeat that in point 2 for stylistic reasons but do note that it’s important. All this results from your freedom of movement within the EU. If she were to travel alone – and not accompany or join you in another EU country – she would be treated like any Jordanian citizen and the answer would be completely different.)

3. The only valid reasons to refuse a visa in these circumstance are either that

   1. the consulate is not satisfied that your wife is covered by the free movement directive (i.e. there are reasons to believe that she is not your wife, that you are not an EU citizen or that you would not be travelling together)
   2. your wife is a “genuine, present and sufficiently serious threat to public policy, public security or public health”
   3. there was abuse or fraud.

   Compared to regular visa application, those are very restrictive rules that do not leave much discretion to the consulate. In any case, there are also some procedural protections: The standard refusal form is not enough, the decision must be fully justified in writing and the burden of proof is on them. The second criteria (“genuine, present and sufficiently serious threat to public policy, public security or public health”) in particular is quite a stringent test and cannot be invoked lightly.

4. If the visa was refused unlawfully, you have a right to lodge an appeal (well, you have a right to lodge an appeal in any case but if the refusal was lawful, that’s futile; you should fix the issue and reapply instead). The exact modalities should be specified in the refusal letter and depend on the country.

   All courts in the European Union (whether in the first instance or on appeal) can either use EU law themselves to invalidate the decision or refer the case to the EUCJ for clarification. This can take a very long time (in France I am told it can take two years to get a decision from the tribunal administratif in Nantes – which is in charge of all visa matters – and that’s without appeal or involvement of the EUCJ).

   In France, you can also always lodge what’s called a “recours gracieux”, which basically means a letter to the authority who took the decision (e.g. the consulate) asking them to reconsider it. That’s much quicker and with good arguments can be quite successful. Of course, it gets pretty technical at this point and hiring a lawyer is probably necessary.

   Finally, the EU SOLVIT system can also help you having your rights recognised by national authorities. If the case is solid and your rights have genuinely been infringed, the results are also quite good and their performance target is to handle a case in 70 days.

Note: I commented on France because that’s what I know best but Spain must have something similar. Whether you need to apply to the French or Spanish consulate depends on which country will be your main destination.

Your wife needs to apply for a Schengen visa from a French or Spanish consulate (depending on your primary destination). However, the visa application is free and will be processed within 15 days

If your non-EU family members need an entry visa, they should apply for one in advance from the consulate or embassy of the country they wish to travel to. If they will be travelling together with you, or joining you in another EU country, their application should be processed quickly and free of charge:

• Countries which are members of the border-free Schengen area should issue visas within 15 days, except in rare cases, when the authorities should provide an explanation of their decision.

• All other countries (Bulgaria, Croatia, Cyprus, Ireland, Romania, UK) should issues visas as quickly as possible.
  The documents your family members need to include in their visa application may vary from country to country. Before travelling, check which these are with the consulate or embassy of the destination country.

(from http://europa.eu/youreurope/citizens/travel/entry-exit/non-eu-family/index_en.htm)