I agree with Alejandro E: the tassels in the Beauchamp jewel are longer. Not only that, the tips of the tassels in the Beauchamp jewel lack the distinctive bell shape in the original jewel. In the Beauchamp jewel the diamonds hang flat.
Below is the original brooch as photographed at the time of the sale of the French Crown jewels.
The jewel sold in 2008 and now in the Louvre.
I have found it impossible to find sharp, high definition photos of either of the Countesses of Beauchamp who were photographed wearing the brooch, but it is clear in all the available photos that the end of the two tassels lack the distinctive bell shape.
It also seems to me that the shape of the bow is different and lacks the fluid shape of the original Kramer jewel.
This photo has been heavily retouched so the shape of the bow is probably somewhat changed.
In this photo the bottom of the bow brooch can be seen. Again it lacks the distinctive bell shape.
1939
Similarly in this portrait the bottom of the tassels lack the distinctive bell shape.
I have never seen any claim by the Lygon/Beauchamp family that their jewel was formerly part of the French Crown jewels.
When Sotheby's auctioned the jewel in 2001 and again when Christie's prepared their catalogue and press releases in 2008, the auction houses would have had definite proof of the provenance. It would have been something which the Friends of the Louvre and the hierarchy at the Louvre would have studied very carefully before handing over so much money. The monetary value of the jewel rests on proving, irrefutably, the provenance of the piece.