When an Rmd file is knitted on Windows 7 by clicking the [Knit] button, non-ASCII characters do not encode correctly in the output files. I experimented with this issue and wrote a report about what I found. My report is available here. The supporting files can be accessed on the master branch of the github repo.
The report does not offer any solutions. It attempts to provide comprehensive data, so that someone who understands the inner workings of R and RStudio might be able to spot clues. The best-case scenario is that an R or RStudio developer, after reading my report, will have an "Ah-ha!" moment and with a few keystrokes will solve all of RStudio's encoding problems on Windows.
It is likely that this is a package issue, but I don't know which package. Near the end of the report I identify nine suspects under the heading, "R v3.4.0 on 32-bit Windows" in the Summary section.
I have already contacted the R team via an e-mail to R-core and a post on nabble. I am going to post something on Yihui's knitr page at github. If other packages might be involved, I hope that someone will forward my report to the appropriate team.