How to put the significant level above the boxplot using Rstudio, and that this can be seen.

General
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5

You can adjust the spacing below and above the plotted data by adjusting the first and second values in expand = expansion(mult = c(0.05,0.1)). By adjusting that and the textsize argument, you can make the display of the p values pretty. I believe 0.05 is the default value for both bottom and top spacing.
Setting fill = Groups colors the interior of the boxes.
Adding theme_bw() sets a white background.

ggplot(DFlng, aes(x = Groups, y = value, fill = Groups)) + geom_boxplot() + 
  facet_wrap(~Param, scales = "free_y") +
  geom_signif(comparisons = list(c("Control", "Treatment"),
                                 c("Control", "Treatment"),
                                 c("Control", "Treatment"),
                                 c("Control", "Treatment"),
                                 c("Control", "Treatment")),
              test = "t.test", textsize = 3) +
  scale_y_continuous(expand = expansion(mult = c(0.05,0.1))) +
  theme_bw()