Caveat: The Home Office has just published their report (dated Summer 2014) called Review of the Balance of Competences between the United Kingdom and the European Union Single Market: Free Movement of Persons which may (or may not) affect policy decisions impacting your question. Not immediately, but possibly in the foreseeable future.
The UK is generally reluctant to honour a French residence permit because the holder is married to you who is a Brit. The UK does not participate in EU residence and/or the Schengen programme. She can apply for a UK visitor visa, and the chances of success are 'iffy' because she's clearly an overstay risk given that you have a home in the UK. Of course, she's entitled to apply, but be aware of the risks.
Two options. The first is what you're already doing: apply for a spouse visa. This lets her come and go for 30 months and it's renewable for another 30 months. After 60 months she can apply for Indefinite Leave (ILR).
The other option is to try the Singh loophole after you have been living with her in France for 6 months. It's a gamble, but if she gets it, it's cost free from there on.
Calling the British Consulate for advice is a waste of time. You will enter a telephone maze of recordings and circular menu options. Consular staff are forbidden (since about 2008) to discuss it with individuals in the first instance. They will route you to their 3rd party contractor who will (astonishingly) charge you by the minute to read their web site to you over the phone.
A BBC article describing the Singh loophole is here: http://www.bbc.co.uk/news/uk-23029195
Adding 27 Feb 2016
Before using the Singh loophole it's wise to consider what may happen if the UK leaves the EU. There is a possibility that those residing in the UK who used Singh may find themselves with a precarious immigration status. The policy has not been drafted, so it is only something to consider. Maybe a tranche of migrants will be required to apply for indefinite leave or maybe they won't. It cannot be predicted and at this point in time it's prudent to consider all the various outcomes. In the event the UK opts out of the EU, they wouldn't get around to even drafting the policy until about 2018 and it would include a transition arrangement anyway.