Could you put a few fir branches into a vase (ask a florist local to your rental to get the branches on 24th, or even on 23rd if you will be there early enough, or a Christmas tree supplier if they would still be open at that stage) and just hang a few decorations from that?
Bring a string of fairy lights and put those up to help decorate.
Window clings also take up very little room in a car and can help make a rental quite festive.
And if you are going making proper Christmas dinner in an unfamiliar kitchen, really really think hard about those tools that you ALWAYS use and whether you want to bring a few key ones with you. (We rent frequently, including at Christmas (although we host a party on 26th of nibbles and don't need to cook the actual turkey dinner), and I have a "self catering (and now camping) box" that is always ready to go with tools that I always want and regularly notice are not there in rentals).
The main contents of that box are:
SHARP knife (I now have a small paring knife, and a medium chopper, both with blades in covers to prevent cuts when rooting in the box)
Vegetable peeler
Corkscrew! and bottle opener, and a bottle sealer as well (we often have a half used bottle to save for tomorrow)
Tin opener
A decent wooden spoon
Small spatula
Pair of Silicon oven mitts
A set of cheap ikea plastic tools - whisk, tongs, serving spoon etc
Small chopping board
Washing up brush
A small cheese grater
And some consumables that I replenish when I get home (whatever has been used up):
J cloth
Travel bottle (100ml) of washing up liquid
Plastic pot scrubber thing (I add a new one for each trip)
Washing powder tablets (3) and dishwasher tablets (at least 6, more if the trip is long)
Small roll of black sacks and 3 small white bin liners
1 emergency loo roll
3 pocket packs of tissues
250ml bottle of olive oil
Salt and pepper mills (the glass type with the mill on top from the supermarket)
Ketchup sachets (leftovers from McD's or Burker King trips) (mayonnaise/vinegar/mustard etc sachets if I get any)
(I also used to bring some sugar sachets from coffee shop trips, but no one uses sugar in our house so we don't bother anymore)
Roll of cling film and roll of tin foil
Handful of sandwich bags (useful for mixing things and marinating things as well as storage in fridge etc or for picnics)
The remains of the box of ice-cube bags - there isn't always an icecube tray but the bags are handy for those rare uses
Box of matches, and 3 instant firelighters in packets
3 nightlight candles (can light them on saucers if no other option around, once small DCs are not running around)
A torch
A few spare batteries - usually just AA, AAA (and D for the portable radio we bring)
Sellotape, a pen and small notebook
And 2 hand towels and 2 tea towels for the kitchen, that get washed and put back in general use (rather than the box) when we get home
And don't be afraid to make life easier - paper napkins and some disposable serving dishes, plastic cups/glasses, extra kitchen towel, pre-grated/pre-sliced cheese etc.
I've made up cake mixes and cookie mixes some years before travelling - weighed out the ingredients into sandwich bags, and out them all together in a larger sandwich bag as "Chocolate cake" or "Cookie mix" or "Pancake mix", and just brought the tin needed. A baking sheet is usually very useful for sausage rolls and other nibbles anyway, or part baked bread, as well as cookies. All you need is a large bowl, wooden spoon, and measure out any wet ingredients to be able to turn out homebaked goodies.
And you can probably do some things at home before travelling as well - things like herb butter can be chopped and mixed together into a log in some greaseproof paper, cookies or meringue bases for desserts can be pre-made and transported etc.
Are you doing it all yourself, or will others turn up to pitch in? Can you pre-order a grocery shop local to the rental, either to collect after you arrive, or (better yet) be delivered?
Think through the menu beforehand, and list EVERY SINGLE THING you need for it. Including salt and pepper, specific herbs, butter or oil, stock or gravy powder or your secret ingredients....EVERYTHING for EVERY course of the main meal, and other things you normally love (so a lime for the G&Ts, or capers to go with smoked salmon, or DH's favourite flavor crisps to nibble on while reading on Boxing Day...). Then develop a master list of everything you need, and how to get it there (online order, bring in the car, shop when you get there, ask other guests to bring...).
Enjoy - it can be fun, once you think about it in advance and do that planning piece!
Sorry this is so epic and off topic to your question 
I just love Christmas whether at home or travelling.