I think I found your problem, you have to define a frame for each "Model File" and "Range File" lines and make them to pack to the top and fill 100% the x axis, then within the frames you add all components justified to the left

# CREATE MODEL FILE FRAME
my $model_info_frame = $mw->Frame->pack( -side => "top", -fill => 'x' 
+);

# Label
$model_info_frame->Label( -text => "Model File : " )->pack( -side => "
+left" );

# Input field
$model_info_frame->Entry(
    -width        => 60,
    -textvariable => \$filename
)->pack( -side => "left" );

# Browse files button
$model_info_frame->Button(
    -text    => "...",
    -command => sub {
        $filename = $mw->getOpenFile( -title => 'File Browser' );
    }
)->pack( -side => "left" );

# CREATE RANGE FILE FRAME
my $range_info_frame = $mw->Frame->pack( -side => "top", -fill => 'x' 
+);

# Label
$range_info_frame->Label( -text => "Range File : " )->pack( -side => "
+left" );

# Input field
$range_info_frame->Entry(
    -width        => 60,
    -textvariable => \$filename
)->pack( -side => "left" );

# Browse files button
$range_info_frame->Button(
    -text    => "...",
    -command => sub {
        $filename = $mw->getOpenFile( -title => 'File Browser' );
    }
)->pack( -side => "left" );
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your code has mixed syntax like grid and pack, use grid to define layouts based on rows and columns