I have experience with long distance cycling in many of the same countries you will be going through (among others Romania, Hungary, Serbia, Croatia, France) and it surprised me as well, but I have the impression that car drivers in Eastern European countries are often much more considerate than their Western European counterparts. I am only speculating, but I guess they are more used to slow-moving vehicles intermingling with regular traffic. At least in Romania and Bulgaria, horse carriages are still common to see on regular roads and most car drivers are very aware that they must overtake with consideration and keep a distance.
I must admit that I tried to avoid larger roads and that most of the 600km I travelled through Romania were on rural roads with not so much traffic, but I also had a few short passages on larger roads with heavy traffic where no other options were feasible, e.g. around Turnu Severin, and I can't remember having any larger issues there either.
Thieves and robbers may of course be a problem anywhere, hearsay about Eastern European countries is perhaps not the best in this regard, but you must just realize that you will have to take risks. I travel mostly alone and if you have a bicycle packed with luggage, luggage there are no means to properly secure, you just have to cope with the fact that many tasks are impossible, even simple things like going to the toilet for a number two, without simply leaving everything you have unattended and hope that it will still be there when you are finished whatever you are doing. That is life.
The only real problems I have had, and I must second Danubian Sailor here, were with dogs. Even quite often. Do not underestimate them. There are occasional stray dogs in the countryside and loose guard dogs in many villages and they are for some, to me not obvious, reason often triggered by cyclists. Expect them to set after you and go for your ankles. Using Google, you will find plenty of suggestions how to deal with the problem, and as a final resort you should be prepared to defend yourself or even hurt the dog as a mean to show that you are stronger.
What has worked for me, but your mileage may vary (also my mileage in the future) is to:
Either outrun them - a dogs stamina is usually not very great or perhaps they decide that the effort to keep up with you is not worth whatever gain they expect from catching you. You should though expect that the dogs can easily reach 25-30 km/h and keep up with you a kilometre or more. That is indeed faster than my 'comfort speed' when cycling, but with a potentially rabies infected biting machine literally on or in my heels, that has usually worked out.
Or, if you realize that you can't outrun them, stop, get off the bicycle and place the bicycle between you and the dogs. Notice that you have to decide for this option with enough distance between yourself and the dogs for you to have time to position the bicycle as a defensive barrier. I think I've only used this option twice and the outcome was very different. The first time was uphill somewhere in the Greek countryside, where I had a single German shepherd lookalike turning up from nowhere and going after me. As soon as I got off the bike, the dog started wagging its tail and turned into a very friendly fellow. As soon as I tried to get onto the bike again, the dog started to snarl and show aggressive behaviour. Don't ask me why it worked, but I solved the problem by walking the bike for a while with the dog following and after a while he lost interest and ran back. The second time was in a village in Romania with a broken gear cable, where I realized that it would not even make sense to try to outrun the two dogs setting after me. Here, it did not help to get off the bike, but the the dogs actually staid on the opposite side of the bike and did not have the guts to go around the bike to attack. I could probaly have solved the situation with pepper spray, which I did not have. I was ready to use the bike lock as a weapon if the dogs really tried to attack, but after a while they lost interest and went back to their home.
Just a word on rabies, in case someone didn't catch my slightly humorous tone in my statement about 'rabies infected biting machines': Rabies is in reality nothing to worry about in the countries OP is going to traverse. There have in total, in all countries along the route, been five cases of human rabies in the last 10 years (one each in Romania, Italy, France, Spain and Portugal). If OP is concerned about rabies anyway, he should get a vaccine in advance and not rely on being able to be bitten in a limb far enough away from the central nervous system that he has time for a post-bite vaccine before the infection reaches an irreversible and fatal stage.
FWIW, I met a bear out in the wild in Romania last year, we were probably not more than 4-5 meter apart, and felt much more in control than with these two dogs. The bear encounter was more like, ups, neither of us ment to disturb the other, if we just forget that we met, we can both go on doing what we were just doing. She was friendly enough though to sit down for a photo before we parted.