France/NIII won't do anything the British are not doing simultaneously or previously. NIII very carefully trimmed his support of the CSA based on what the British were doing. Absent something like the Trent Affair snowballing in to a direct conflict between the USA and the UK I don't see Britain getting militarily involved against the USA, even if they decide to recognize the independence of the CSA. Even with recognition of the CSA, the UK is unlikely to try and use force to break the blockade of the south, because the blockade is a close blockade and in accordance with the laws of war as they existed then. It appears from the evidence that the UK (and subsequently France) were not going to formally declare the CSA to be independent unless and until the military situation on the ground became clear that the odds were very much they were going to succeed.
The Confederate leaders put great store in the possibility of French and British recognition. While this would potentially give them greater access to credit, and possibly more open purchases of arms, the concept of the RN breaking the Union blockade for the CSA or other direct military intervention was not going to happen outside of direct US-UK war scenario. Had the CSA succeeded, in the aftermath of a successful secession, treaties between the CSA and UK and/or the CSA and France would not be unreasonable - France more likely than the UK as the UK had a tendency not to get in to fixed defense treaties.
The dream of the UK or UK/France coming in on white horses to ensure Confederate victory was a persistent but unrealistic dream of Confederate political leaders from the get-go as evidenced by the early application of the cotton embargo to force the UK and France to aid the CSA to ensure their supply of cotton. Not the only bit of magical thinking the CSA upper levels had.