If you have GNU awk (available from the repository via package gawk), which supports multi-dimensional arrays, you could do

gawk 'NR==FNR {a[$1][$2]++; next} $1 in a {for (x in a[$1]) print $0, x}' OFS="\t" file_2.txt file_1.txt

Ex.

$ gawk 'NR==FNR {a[$1][$2]++; next} $1 in a {for (x in a[$1]) print $0, x}' OFS="\t" file_2.txt file_1.txt
apple   2.5     5       7.2     :::N
great   3.8     10      3.6     :::ADJ
see     7.6     3       4.9     :::V
tree    5.4     11      5       :::N
back    8.9     2       2.1     :::ADJ
back    8.9     2       2.1     :::N

Otherwise, if output order is not important the easiest solution is probably to use the join command instead:

$ join -t $'\t' <(sort file_1.txt) <(sort file_2.txt)
apple   2.5     5       7.2     :::N
back    8.9     2       2.1     :::ADJ
back    8.9     2       2.1     :::N
great   3.8     10      3.6     :::ADJ
see     7.6     3       4.9     :::V
tree    5.4     11      5       :::N

One possible way to do it

A while back I created a function specifically for that purpose which I keep in my .bashrc, and can be adapted into a script. You should be taking advantage of positional parameters so that users can put filenames on command-line. Here's my original function:

swap_files() {
    if [ $# -ne 2 ]
    then
        echo "Usage: swap_files file1 file2"
    else
        local TMPFILE=$(mktemp) 
        mv -- "$1" "$TMPFILE"
        mv -- "$2" "$1"
        mv -- "$TMPFILE" "$2"
    fi
}

You can get rid of swap_files(){ declaration, local keyword, and closing }, and turn it into a script - just add #!/bin/bash at the top. Granted there's tons of things that can be improved, but at the very basic level that's about as simple as swapping gets (which by the way is frequently taught in C to swap array items, but that's just a tangent topic).

#!/bin/bash
if [ $# -ne 2 ]
then
    printf "Usage: swap_files file1 file2\n" > /dev/stderr
else
    TMPFILE=$(mktemp)
    mv -- "$1" "$TMPFILE"
    mv -- "$2" "$1"
    mv -- "$TMPFILE" "$2"
fi

Of course, remember to quote the positional parameters if filenames contain spaces. Like so:

swap_files 'file 1' 'file 2'

Note the use of -- to avoid issues with filenames that have leading - in them. A better way would be to get into habit of referencing files in current working directory with ./, especially if you are using globstar * ( globstar is not relevant in this question, but it's worth mentioning if we're talking about filenames with leading -). Besides,./ way is more portable, since some versions of mv such as on FreeBSD don't have the -- option.

As suggested by terdon in the comments, we can also create temp file in first file's parent folder to avoid moving files across filesystems.

#!/bin/bash
if [ $# -ne 2 ]
then
    printf "Usage: swap_files file1 file2\n" > /dev/stderr
else
    file1_dir=${1%/*}
    # just in case there were no slashes removed, assume cwd
    if [ "$file1_dir" = "$1" ]; then
        file1_dir="."
    fi
    tmpfile=$(mktemp -p "$file1_dir" )
    mv -- "$1" "$tmpfile"
    mv -- "$2" "$1"
    mv -- "$tmpfile" "$2"
fi

Your script and things to improve

1. Redundant variable assignment

file1=$file1
file2=$file2

This portion assigns $file1 variable to ... file1 variable; there's two problems with this - assigning variable to itself is redundant, and it doesn't exist to begin with, there's no declaration of that variable earlier in the script.

2. Beware of word splitting with read

Here's what's going to happen if your user tries to put in even quoted items into your read command:

$ read file1 file2
'one potato' 'two potato'

$ echo "$file1"
'one

$ echo "$file2"
potato' 'two potato'

In accordance with shell behavior, the shell splits everything that is read on stdin and tries to fit in each word into corresponding variables, and if words exceed number of variables - it tries to push everything into the last variable. I'd recommend you read in each file , one at a time.

3. Copying to itself is an error

You're doing

cp $file1 $file1;

That'll produce an error

$ cp input.txt input.txt
cp: 'input.txt' and 'input.txt' are the same file

Perhaps you wanted to do

cp "$file1" "$file1".tmp

Or just make use of mktemp command as I did. Also note the quoting of variables to prevent word splitting.

Other fun ways to do it

Did you know that you can cat any file with redirection to make a copy? So using mv or cp isn't the only way. Something like this:

$ cat ./wallpaper.jpg > wallpaper.jpg.tmp
$ cat ./screenshot.jpg > wallpaper.jpg
$ cat ./wallpaper.jpg.tmp > ./screenshot.jpg