Welcome to Flyertalk, Dan Kunze

Given the unpalatable wait with your Plan B, I'd steam ahead with the 60 minute connection. It will be somewhat rushed but if you are happy being proactive (and forceful if necessary) it is possible to exit the incoming aircraft and complete the transfer formalities (conformance and security) in under 30 minutes. My advice would be to let the crew know, before landing, you have a very short connection. They may be able to clear a path to the exit door for you so you're among the first off the aircraft. Easy to do in theory but not always possible in practice. Do the same at security. You can expect your Toulouse flight to start boarding at 07:25 so use this as your frame of reference.

BA should provide you with personal transfer assistance should they think your connection is in peril, eg. late inbound but not too late to rule a misconnection.