The link Paris-Berlin was called Jellyfish by the people of Bletchley Park. This link was first detected in January ‘44 and it used the Lorenz SZ-42 cipher machine. Jellyfish connected OB WEST-Commander in Chief West with the OKH so this traffic was important for the operation Overlord planners.
The official history ‘British Intelligence in the Second World War’ vol3 part 1 says that this traffic was intercepted since January 1944 and first ‘broken’ in March. Appendix 2 says that ‘in the months before the Normandy landings its decrypts were to be of the greatest value’.
This might be an exaggeration. The Jellyfish ‘break’ was a great codebreaking success but it did not have a strategic effect on operations and planning for several reasons. The main one was that the ‘break’ took place too late in the planning process. By March/April the Overlord plan could not be altered, only small changes could be made based on the new intelligence. This problem was compounded by the long delay in decrypting the SZ42 messages. Usually it took a week or more to solve them.
In addition a lot of the Information on the Jellyfish decrypts could not be understood. The Germans used a special form for their strength reports and this could not be ‘decoded’ by the British.
According to ‘British Intelligence in the Second World War’ vol3 part 2 the main contribution of the Jellyfish intelligence was to ensure that the Fortitude deception was successful and in late May to change the landing sites for the aerial landings by the US airborne divisions so they would not fall directly on top of German occupied areas.
I’ve already given my opinion on the Fortitude operation here. As for the airborne operation in practice the transport planes were unable to drop the paratroopers in the correct positions, so the outcome was the same.
The people of Bletchley Park ran out of luck in June. On June 10 they lost access to Jellyfish and in July they also lost the Berlin-Rome link. They would manage to solve them again in September. This setback was caused by an improvement in the German security procedures (P5 limitations and daily change of the internal settings).
Sources: ‘British Intelligence in the Second World War’ vol3 part1 appendix 2, ‘Decrypted Secrets: Methods and Maxims of Cryptology’, ‘The Normandy Campaign 1944: Sixty Years On’ chapter 14
Acknowledgements: I have to thank Marek Grajek for pointing out that the loss of Jellyfish was not only attributable to ‘P5 limitations’ but mainly to the daily change of machine settings for the SZ42 (positions of the pins in the wheels). Prior to June the internal settings were changed monthly.