If you are really just dealing with pairs of columns and you don't want a "variable" or "value" column, then maybe you can just do:
matrix(c(t(df)), ncol = 2, byrow = TRUE)
##      [,1]       [,2]     
## [1,] "20171201" "100,00€"
## [2,] "20171204" "110,00€"
## [3,] "20171202" "101,00€"
## [4,] "20171205" "110,00€"
From there, convert to data.frame or data.table or tbl or whatever you prefer to work with....
But, I don't know why you wouldn't just do:
library(data.table)
melt(as.data.table(df), measure.vars = patterns("Reference", "Amount"), 
     value.name = c("Reference", "Amount"))[, variable := NULL][]
#    Reference  Amount
# 1:  20171201 100,00€
# 2:  20171202 101,00€
# 3:  20171204 110,00€
# 4:  20171205 110,00€
Sample data (from a deleted answer by @Florian):
df = read.table(text='Reference   Amount    Reference.2   Amount.2
1:   20171201     100,00€    20171204    110,00€
2:   20171202     101,00€    20171205    110,00€',header=T)