France offers to share nuclear deterrent with UK

France has offered to form a joint nuclear deterrent with the UK with shared submarine patrols according to reports. The UK is so far against the idea because of soverignty issues though if the SSBN force is reduced from 4 submarines to 3 it may be a pooled force will be required to absolutely guarantee a continuous deterrent. The question would be of course what if we wanted to nuke someone but a French boat was on patrol at the time and refused to fire. It is likely though that any attack on either country would require a response from both countries.