SQL Double Conditional SELECT without repeating values within a column

I would use ROW_NUMBER here:

WITH cte AS (
    SELECT *, ROW_NUMBER() OVER (PARTITION BY PropertyName
                                 ORDER BY CASE LANGUAGE WHEN 'fr' THEN 1 ELSE 2 END) rn
    FROM Details
    WHERE Language = 'fr' OR IsDefault = 1
)

SELECT Language, IsDefault, PropertyName
FROM cte
WHERE rn = 1;

Demo

The logic above is to use a single query to generate a result set with all candidate records. We also turn out a row number, per property, based on an ordering where French properties always rank higher (read: row number is lower) than properties from all other countries. We retain only one record per property.

You can go for UNION ALL also to achieve the result.

;cte_fr AS
(SELECT PropertyName, IsDefault, Language
FROM Details
WHERE Language = 'Fr')
select propertyname, isdefault,language from cte_fr
UNION ALL
select propertyname, isdefault,language from Details as d
WHERE NOT EXISTS (
select * from CTE_FR
WHERE PropertyName = d.PropertyName
)
and d.IsDefault = 1;

You can get your desired results simply by grouping,

select  Max([Language]), Max(IsDefault), Max(PropertyName)
from Details
where [language]='fr' or ([language] !='fr' and isdefault='True')
group by PropertyName