Most histories say that the Dunkerque & Strasbourg were built to counter the Deutschland class. The Dunkerque was laid down in the last days of 1932 and the Cavour didn't start rebuild until Oct 1933. I have no idea how leaky the Italian design offices were to French spies.
The French and Italians were trying to one up each other with Destroyers and Cruisers and came up with some of the worst designs possible. Egg shells armed with hammers may have been borrowed from the British WW I battlecruisers but some of these ships were even less balanced.
Yes that is the way it is portrayed in most histories. But that puts the focus on Germany and ignores what was going on between Italy & France at the time. It is more complicated than portrayed. The appearance of the Deutshland class has some influence on the French ships but they were not built simply to counter them.
And on looking back I have laid out the order of the Franco / Italian battle less than clearly.
Go back to the Washington Conference negotiations in 1921/22 and you will see that the original proposals would have left the French and the Italians with 7/6 old pre-Jutland dreadnought battleships of limited use plus a few pre-dreadnoughts that were already useless. As a result they secured the ability to lay down replacement tonnage before other nations. Each got an entitlement to 35,000 tons in 1927 & 1929.
The French began to study new battleship designs in 1926, with proposals ranging from 17,500 tons in 1926 through 37,000 tons in in 1927/28 to 23,333 tons in 1930. They faced 3 limitations:-
1. Technical - the larger designs would exceed then current building facilities. As it was Dunkerque was built in two parts and joined after launch. Richelieu was built in 3 parts.
2. Financial - the Govt was limiting expenditure
3. Political - this was an era of disarmament. As a principal proponent of disarmament she could not have been seen to start building a new batch of super battleships up to the tonnage limits allowed (35,000 tons). At the same time by 1930 Britain was proposing a 25,000 ton /12" gun limit on battleships ahead of the 1930 London Conference, which France wanted to support. Both France and Italy came out of London retaining the right to build that new tonnage while the battleship holiday for other nations was extended until the end of 1936.
So with aging tonnage France needed to begin building new ASAP. But what size? 23,333 tons gave them 3 ships with 305mm guns within their 70,000 ton allowance. But they needed to future proof the design and this is where the influence of the Deutschland becomes apparent. The decision to increase to 26,500 tons allowed an increase in gun calibre to 330mm from 305mm v the 280mm of Deutschland and an increase in protection against the German weapon. Until that point Jordan & Dumas make no mention of Deutschland as an influence in French designs.
But you are still talking about a ship that is 26,000 tons / 29.5 knots v a Deutschland of c12,000 tons / 26 knots. So they were clearly intended to be much more than simply a "counter" to the heavy cruiser sized / panzerschiffe Deutschland. Dunkerque was laid down in Dec 1932. Before a second identical ship could be ordered Italy had announced her decision to proceed with the Littorios and the Germans had announced plans for Deutschland number 4 (it became Scarnhorst in due course). In order not to suffer delays by designing a new vessel, the Dunkerque design was beefed up and Strasbourg (27,300 tons) laid down in Nov 1934.
Meanwhile over in Italy, the focus in the 1920s was on naval spending to create a fleet to match France, so it was the end of the 1920s before thoughts turned to replacement battleship tonnage at which point 23,000 ton designs were considered. Because of ongoing political uncertainties in the early 1930s the Italians decided to hang fire on new construction and in Oct 1933 adopted the interim solution of rebuilding Cesare & Cavour. At this point there was a lot of negotiations going on between Italy & France following the London Conference brokered at least some of the time by Britain & America, to prevent the two nations getting into an arms race, which might then have forced the collapse of the Treaty system.
In mid-1934 the Italians opted for a full 35,000 ton design, the Littorios, laying down 2 ships on 28th Oct 1934. Even after this Franco - Italian negotiations continued with a view to reversing this but ultimately nothing happened. The Italians then looked towards building a fleet of 8 battleships (4 Littorios & 4 reconstructions). So in 1935 began the reconstruction of Doria & Duilo and in 1938 the construction of a second pair of Littorios.
Following the Italian decision to proceed with the first pair of Littorios, France immediately began the design of a ship to match them. That became the Richelieu class. With Richelieu laid down in Oct 1935 the French were technically in breach of their Treaty limits and even more so after Jean Bart was laid down 3 weeks before the Washington Treaty expired at the end of 1936. But it was complicated by France onlysigning up to bits of the 1930 London Treaty and again politics was playing its part because the French were annoyed by the Anglo-German Naval Agreement of 1935 allowing Germany to build up to 35% of the RN tonnage.
After that French attention seems to shift focus more towards Germany than Italy. With Germany changing the design of Deutschlands 4 & 5 to the larger Scharnhorst class (laid down mid-1935 after the Strasbourg) to match the Dunkerques and then the Bismarcks in 1936, France then follows up with plans for another pair of 35,000 tonners based on the Richelieu design in 1938. By then France is having to face the prospect of potential enemies in both the Atlantic & the Med.
Sources:-
"French Battleships 1922-1956" by John Jordan & Rubert Dumas
"Littorio Class Italy's Last & Largest Battleships 1937-1948" Erminio Bagnasco & Augusto de Toro
The second of these goes into detail about the various negotiations between the French & Italians about naval construction between 1930 & 1935.