Row wise Sorting in R

If we need only to sort by rows, use apply with MARGIN=1 and assign the output back to the original columns after transposing the output.

df1[-1] <- t(apply(df1[-1], 1, 
        FUN=function(x) sort(x, decreasing=TRUE)))

df1
#   Name English Math French
# 1 John      86   78     56
# 2  Sam      97   86     79
# 3 Viru      93   44     34

NOTE: But we may need to change the column names as sorting by row gives the new sorted values.

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Another option will be use apply separately to get the column names and the values, with Map we get the corresponding columns, cbind with the first column to have the output.

nMat <- `dim<-`(names(df1)[-1][t(apply(df1[-1], 1,  
        order, decreasing=TRUE))], dim(df1[-1]))
vMat <- t(apply(df1[-1], 1,  sort, decreasing=TRUE))
cbind(df1[1], data.frame(Map(cbind, as.data.frame(nMat,
   stringsAsFactors=FALSE), as.data.frame(vMat))))
#  Name    V1.1 V1.2   V2.1 V2.2    V3.1 V3.2
#1 John  French   86   Math   78 English   56
#2  Sam    Math   97 French   86 English   79
#3 Viru English   93   Math   44  French   34

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Or another option is data.table. We melt the 'wide' format to 'long' format, grouped by 'Name', we order the 'value' in decreasing order in 'i', get the Subset of Data.table (.SD), create a new column ('N'), grouped by 'Name' and use dcast to convert from 'long' to 'wide'.

library(data.table)
dcast(melt(setDT(df1), id.var='Name')[order(-value), 
  .SD, Name][, N:=paste0("Col", 1:.N) , .(Name)],
    Name~N, value.var=c("variable", "value"))
#   Name variable_Col1 variable_Col2 variable_Col3 value_Col1 value_Col2 value_Col3
#1: John        French          Math       English         86         78         56
#2:  Sam          Math        French       English         97         86         79
#3: Viru       English          Math        French         93         44         34

EDIT: The above data.table solution will not work in case you have 10 or more columns with values, because then col10 will preceed col2 in the ordering, even though higher values will be stored in col2. To resolve this issue, you can use just number for the names of your new columns as in:

dcast(melt(setDT(df1), id.var='Name')[order(-value), 
      .SD, Name][, N:=1:.N , .(Name)],
        Name~N, value.var=c("variable", "value"))

You can try:

cbind(x[1],matrix(paste(colnames(x)[apply(x[,2:4],1,order,decreasing=TRUE)+1],
      apply(x[,2:4],1,sort,decreasing=TRUE)),ncol=3,byrow=TRUE))
#  Name          1         2          3
#1 John  French 86   Math 78 English 56
#2  Sam    Math 97 French 86 English 79
#3 Viru English 93   Math 44  French 34