If you are travelling from Cham to Paris you should book Cham to Paris, not Zurich to Paris and Cham to Zurich separately.
If you book Cham - Paris in one transaction, and take the trains suggested by the SBB you will have protected connections. If you split, and plan a connection under the minimum connection time (which is 6 minutes for Zurich) you will not be protected in case of a delay.
The direct trains from Zurich to Paris are running on that day btw. If you want an earlier connection you can go via Basel and Strasbourg, with a departure at 5:12 and an arrival at 10:36…
But in your place I would take the 6:59 from Zurich, for which you would leave Cham at 6:14…
