Couple things...
1) Your client filed a F.8233 with Pro Golfer to certify himself as being eligible for treaty exemption under the Independent Personal Services article (of possibly the Czech Republic according to your info above).  It is not uncommon for caddies to be classified as an independent contractor but there have been legal challenges to that position.  I'd re-evaluate the relationship based on facts and languages in the agreement rather than relying solely on that declaration.  Even you mentioned that he was "employed" by a Pro Golfer.
2) You mentioned that your client is on a R-1 visa.  This is a visa for nonimmigration religious workers.  How would your client be on this visa and have earned income as a caddie?
3) Assuming your client was an independent contractor in fact, question remains whether he has a PE in the US as defined in the treaty article, which would expose him to US tax even if his US presence falls within the threshold.
4) You mentioned he is a French national but is claiming treaty benefits as a tax resident of the Czech Republic.  I would examine all the facts carefully based on Article 4 as well as the status of foreign tax filing to determine his eligibility under either treaty.
5) Even in the event the income is exempt under the Independent Personal Services article, a 1042-S was issued, and assuming he not no other US-ECI or FDAP income that would require the filing a return, a 1040NR would, nonetheless, be required for treaty disclosure.
6) Some states (such as CA) do not recognize federal income tax treaties. You'd need to review the state(s) in which he performed services and determine whether income tax return(s) will need to be filed and if taxes would be owed.

Seems like you have a bit more research to do before preparing his US return(s).