That pamphlet confused me. What country? It’s in English and French, suggesting Canada, but it refers to the Department of Health and Human Services and county/state, which I think is American.
(I can’t see the first picture.)
U.S. Check your passport. It’s in English and French. AIUI (or as I assume) French was once the international language. Now it’s English and French.
As far as I can tell, it’s a US document (issued by the US CDC) but in conformance to a diplomatically negotiated international standard via the World Health Organization.
The French legends reflect the international nature of the document. I think French has a status as the common language of diplomacy that goes back centuries.
I’m a Canadian, so of course it’s in English and French 
It seems French is still seen as a language of international diplomacy.
In Frenchmens fevered dreams…elsewhere not so much. 
Records in the old days were all kept on paper, and I’d be very surprised if anyone even knows if they exist anymore much less their exact location. The good news is that, these days, your kids’ (grandkids’?) records are all kept in Powerschool. Parents have a Powerschool parent signin portal through which they have access to their children’s grades, attendance, health records, etc.
There was a pertussis outbreak in my old town in the 00s, thanks in no small part to the large unvaccinated Amish population. Anyway, the health department advertised they they would give vaccines to anyone who was qualified, $15 cash or free with Medicare Part B or Medicaid. A TV station went there and talked to a few people, and they were all saying things like “I’m not all that concerned about myself, but I work at a gas station/I have grandchildren/I’m a neighborhood child care provider”, that kind of thing.
The hospital I worked at gave lots of MMR shots to moms upon discharge (it contains live virus and cannot be given during pregnancy) and a lot of DTaPs to them, and their husbands too. The Hep B vaccine was also part of the newborn protocol, and I don’t know what percentage of the parents allowed them for their babies, but it wasn’t very high, because whenever the techs went upstairs to clean out the refrigerator, they would always bring dozens of doses back to the pharmacy to be discarded, because we had no way or knowing if they had been in a patient’s room or how long they had been out of the refrigerator. The 3-shot series is required for school attendance, and many licensed day cares require at least the first shot.